Daoxing Xia
Professor Emeritus
Research Interests
Operator Theory and its Application, Functional Analysis, Applied Mathematics, Modern Mathematical Physics, Theory of Functions and Theory of Probability
Publications
Books and Monographs
(with S. Yan) Spectral Theory of Linear Operators, Press Acad. Sinica, Beijing, (1987), 1-460.
(with S. Yan, W. Su and Y. Tong) The Second of Functional Analysis, Press High. Edu., Beijing, (1986). New edition (2009).
(with Y.L. Yang) An Invitation to the Theory of Linear Topological Spaces, Sci. Tech. Press Shanghai (1986) 1-321.
Spectral Theory of Hypononnal Operators, Sci. Tech. Press, Shanghai, (1981), Birkhauser Verlag, Basel-Boston-Stuttgart, (1983) 1-241.
(with S. Yan. Z. Wu and W. Su) Theory of a Real Variable and Functional Analysis, Press Acad. Sinica, Beijing, (1980) 1-448.
Measures and Integration on Infinite-dimensional spaces, Sci. Tech. Press Shanghai, (1965), Acad. Press, N.Y., London (1972) 1-425. New edition, China High Education Press, Bejing (2009).
(with S. Yan, Z. Wu, and W. Su) Theory of Functions of a Real Variable and Essentials of Functional Analysis, Sci. Tech. Press Shanghai (1956), 1-747. New edition, China Higher Education Press, Beijing (2010).Analytic Theory of Subnormal Operator (in Chinese), China Higher Education Press, Beijing, Aug. 2012; (in English), World Scientific, New Jersey, London, Singapore, 2014.
Articles
"Commutator formula for subnormal tuple of operators," Integr. Oper. Theory, 83 (2015), 381-392. PDF
"A model of some class of operators", Integr. Equat. Oper. Theory, 81 (2015), 237-254. PDF
"A note on the complete unitary invariant for some subnormal operators,", Integr. Equat. Oper. Theory, 77 (2013), 291-298. PDF
"Analytic theory of hyponormal operators with rank one self-commutators", Integr. Equat. Oper. Theory, 75 (2013), 573-589. PDF
"Operator identities for subnormal tuples of operators," In "A Panorama of Modern Operator Theory and Related Topics," edited by H. Dym, M.A. Kaashoek, P. Lancaster, H. Langer, and L. Lerer in the series "Operator Theory: Advances and Applications," Vol. 218 (2012), 613-638, Birkhauser Verlag, Basel-Boston-Stuttgart. PDF
"Determinant formula and trace formula for some finite rank perturbation of Heisenberg commutation relation," Integr. Equat. Oper. Theory, 60(2008), 573-590. PDF
"Determinant formula for the trace class perturbation of Heisenberg commutation relation," Integr. Equat. Oper. Theory, 56 (2006), 571-585. PDF
"Chern characters associated with almost commuting algebras," Proc. Amer. Math. Soc. 125 (1997), 507-514. PDF
"Hyponormal operators with finite rank self-commutators and quadrature domains," Jour. Math. Anal. Appl. 203 (1996), 540-559. PDF
"On pure subnormal operators with finite rank self-commutators and related operator tuples," Integ. Eq. Opera Theory, 24 (1996), 107-125. PDF
"Generalized cyclic cohomology associated with deformed commutators," Proc. Amer.Math. Soc. 124 (1996), 1743-1753. PDF
"Trace formulas and complete unitary invariants for some k-tuples of commuting operators," Contem. Math. 185 (1995) 367-380. PDF
"Trace formulas for the perturbation of some partial differential operators and cyclic cocycles on generalized Heisenberg group," Opera Theory. Adv. and Appl. 62, Birkhiiuser, Verlag, Basel (1993), 209-231. PDF
"Trace formula for a class of subnormal tuple of operators,"Integr. Equ. Opera Theory. 17 (1993), 417-439. PDF
"A note on the trace formulas for almost commuting operators," Proc. Amer. Math. Soc. 16 (1992) 135-141. PDF
"Complete unitary invariant for some subnormal operator,"Integr. Equ. Opera Theory. 15 (1992), 154-166. PDF
(with J. Pincus) "A trace formula for subnormal operator tuples," Integr. Equ. Opera Theory. 14 (1991), 390-399. PDF
"Analytic theory of hyponormal operators with rank one self-commutators", Integr. Equat. Oper. Theory, 75 (2013), 573-589. PDF
"Operator identities for subnormal tuples of operators," In "A Panorama of Modern Operator Theory and Related Topics," edited by H. Dym, M.A. Kaashoek, P. Lancaster, H. Langer, and L. Lerer in the series "Operator Theory: Advances and Applications," Vol. 218 (2012), 613-638, Birkhauser Verlag, Basel-Boston-Stuttgart. PDF
"Determinant formula and trace formula for some finite rank perturbation of Heisenberg commutation relation," Integr. Equat. Oper. Theory, 60(2008), 573-590. PDF
"Determinant formula for the trace class perturbation of Heisenberg commutation relation," Integr. Equat. Oper. Theory, 56 (2006), 571-585. PDF
"Right spectrum and trace formula of subnormal tuple of operators of finite type, Integr. Equ. Oper. Theory, 55 (2006), 439-452. PDF
"On a class of operators of finite type," to appear in Integr. Equ. Oper. Theory, 54 (2006), 131-150. PDF
"Hyponormal operators with rank one self-commutators,"Integr. Equ. Oper. Theory, 48 (2004) 115-135. PDF
"Trace formulas for some operators related to quadrature domains in Riemann surfaces," Integr. Equ. Oper. Theory, 47(2003) 123-130. PDF
(with S.A. Stewart) "A class of subnormal operators with finite rank self-commutators," Integr. Equ. Opera Theory, 44 (2002) 370-382. PDF
(with D. Zheng) "Compact products of Hankel operators,"Integr. Equ. Opera Theory, 38 (2001) 357-375. PDF
"On the rank one perturbations of the Heisenberg commutation relation and unbounded subnormal operators," Integr. Eq. Opera Theory. 37 (2000), 487-504 PDF
"On a class of operators with finite rank self-commutators,"Integr. Equ. Opera Theory 33 (1999), 489-506. PDF
(with D. Zheng) "Products of Hankel Operators," Integr. Equ. Opera Theory. 29 (1997), 339-363. PDF
"Chern characters associated with almost commuting algebras," Proc. Amer. Math. Soc. 125 (1997), 507-514. PDF
"Hyponormal operators with finite rank self-commutators and quadrature domains," Jour. Math. Anal. Appl. 203 (1996), 540-559. PDF
"On pure subnormal operators with finite rank self-commutators and related operator tuples," Integ. Eq. Opera Theory, 24 (1996), 107-125. PDF
"Generalized cyclic cohomology associated with deformed commutators," Proc. Amer.Math. Soc. 124 (1996), 1743-1753. PDF
"Trace formulas and complete unitary invariants for some k-tuples of commuting operators," Contem. Math. 185 (1995) 367-380. PDF
"Trace formulas for the perturbation of some partial differential operators and cyclic cocycles on generalized Heisenberg group," Opera Theory. Adv. and Appl. 62, Birkhiiuser, Verlag, Basel (1993), 209-231. PDF
"Trace formula for a class of subnormal tuple of operators,"Integr. Equ. Opera Theory. 17 (1993), 417-439. PDF
"A note on the trace formulas for almost commuting operators," Proc. Amer. Math. Soc. 16 (1992) 135-141. PDF
"Complete unitary invariant for some subnormal operator,"Integr. Equ. Opera Theory. 15 (1992), 154-166. PDF
"Trace formulas for almost commuting operators, cyclic cohomology and subnormal operators," Integr. Equ. Op. Theory. 14 (1991), 276-198. PDF
"Some trace formulas for almost unperturbed SchrOdinger pairs of operators," Proc. Amer. Math. Soc. 112 (1991), 755-764. PDF
"Principal distribution for almost unpertubed Shrodinger pair of operators," Proc. Amer. Math. Soc. 112 (1991), 745-754. PDF
"On some classes of hypo normal tuples of commuting operators," Oper. Theory: Advances and Applications 48, Birkhiiuser, Verlag, Basel (1990), 423-448. PDF
"Analytic theory of subnormal n-tuple of operators," Proc. of Symp. in Pure Math. 51 (1990), part 1, 617-640.
"Cyclic cohomology and k-theory associated with difference operators," Rocky Mtn. Jour. Math. 20 (1990), 637-650.
(with J. Pincus) "Toeplitz type operators, determining functions, principal functions and trace formulas," Jour. Funct. Anal. 88 (1990), 1-63. PDF
(with A. Aluthge) "A trace estimate of (T*T)^P -(TT*)^P,"Integr. Equ. Oper. Theory. 12 (1989), 300-303. PDF
"On the almost unperturbed Schrodinger pair of operators,"Integr. Equ. Oper. Theo. 12 (1989), 241-279. PDF
"Analytic theory of subnormal operators," Integr. Equ. Oper. Theory. 10 (1987), 880-903. PDF
"Cyclic cohomology associated with difference operators and anti-commutators," Integr. Equ. Oper. Theory. 10 (1987),739-750. PDF
"The analytic model of a subnormal operator," Integ. Equ. Oper. Theory. 10 (1987), 258-289. PDF
"Trace formula for almost Lie algebra of operators and cyclic one cocyles," Lecture Notes in Pure and Applied Mathematics 107, Nonlinear and Convex Analysis (1987) 299-308. PDF
"Trace formula for almost Lie group of operators and cyclic one cocyles," Integr. Equ. Oper. Theory. 9 (1986), 570-587. PDF
"Trace formula for almost Lie algebra of operators," Integr. Equ. Oper. Theory. 8 (1985), 854-881. PDF
"Anti-commutators and the related trace formulas," Integr. Equ. Oper. Theory. 8 (1985), 119-136. PDF
(with J. Pincus and J. Xia) "The analytic model of a hyponormal operator with rank one self-commutator," Integr. Equ. Oper. Theory. 8 (1984) 879-893. PDF 1 PDF 2
"On locally bounded topological algebras," Sci. Sinica 13 (1984), 375-390.
"On the semi-hyponormal n-tuple of operators," Integr. Equ. Oper. Theory. 6 (1983), 879-898. PDF
(with R. Curto and P. Muhly) "A trace estimate of the p-hyponormal operators," Integr. Equ. Oper. Theory. 6 (1983), 507-514. PDF
"On the kernels associated with a class of hypo normal operators," Integr. Equ. Oper. Theory. 6 (1983), 444-452. PDF
"On the analytic model of a class of hyponormal operators,"Integr. Equ. Oper. Theory. 6 (1983), 134-157. PDF
"On the spectrum of hyponormal or semi-hyponormal operators," J. Oper. Theory. 5 (1981), 257-266. PDF
"Spectral mapping of hyponormal or semi-hyponormal operators," Math. Anal. App. 79 (1981), 409-427. PDF
(with S.Li) "On functional transformation of semi-hyponormal operators," Chinese Ann. Math. 1 (1981), 501-504. PDF
"On the Toeplitz operator related to the scattering operator of a semi-hyponormal operator," Acta Math. Sci. 1 (1981), 77-82. PDF
(with J. Pincus) "Mosaic and principal functions of hyponormal and semi-hyponormal operators," Integr. Equ. Oper. Theory 4 (1981), 134-149. PDF
"On the representation of the local current algebra," Lecturer Notes on Math. Physics, (1980), 311-315. PDF
(with S.Li) "On the functional transformation of hyponormal operators," Keuxue Tongbao 25 (1980), 625-627. PDF
"On the scattering operator with indefmite metric,"Mathematical Problems in Theoretical Physics, edited by K. Osterwalder, Springer-Verlag, 1980. PDF
"On the characteristic function of semi-hyponormal operators,"Chinese Ann. Math. 1 (1980), 1-8. PDF
"On the non-normal operators-semi-hyponormal operators,"Acta Sci. Sinica 23 (1980), 700-713. PDF
"On the invariant subspaces of contraction operator," Jour. Fudan Univ. 1 (1979), 1-9. PDF
"On the representation of locally current algebras and group of diffeomorphisms," Acta Sci. Sinica, Special Issue II (1979), 149-160. PDF
"On the commutational relation in the global gauge theory for group U(I)," Jour. Fudan Univ. 2 (1978),8-13. PDF
"On non-normal operators (II)," Acta Math. Sinica 21 (1978), 187-189. PDF
"On the quantization of global gauge fields (I)," Jour. Fudan Univ. 4 (1977), 13-21. PDF
(with S. Yan) "On field strengths, sources and gauge potentials of Yang-Mill's field," Kexue Tongbao 22 (1977), 427-430, PDFJour. Fudan Univ. 1 (1977), 80-89. PDF
"On field strengths and gauge potentials of Yang-Mill's fields,"Acta Sci. Sinica 20 (1977), 145-157.
"On the scattering problem concerning indefinite metric or with intermediate system," Acta Math. Sinica 19 (1976), 39-51, 129-143.
"On the scattering problem concerning indefinite metric," Acta Sci. Sinica 18 (1975),165-183. PDF
"Abstract harmonic analysis on the quasi-invariant measures,"Collected Works on Mathematics of Fudan Univ., (1966), 112-130.
"On completely non-unitary contractions," Jour. Fudan Univ.10 (1965).
"On some properties of quasi-invariant measures," Acta Math. Sinica 6 (1965), 382-392.
"Positive-definite functions on commutative topological groups with quasi-invariant measures," Acta Math. Sinica 5 (1964), 369-381, Acta Sci. Sinica 14 (1965), 653-665.
"On the quasi-invariant measures in linear topological spaces,"Jour. Fudan Univ. 83 (1963), 273-277.
"On the equivalence of a class of Gaussian measures," Jour. Fudan Univ. 8 (1963), 151-161.
"On non-normal oprators (I)," Acta Math. Sinica 3 (1963), 232-246.
"On conditionally positive-defmite generalized functions," Sci. Sinica 119 (1962), 1147-1168, Acta. Math. Sinica 113 (1961), 193-201.
(with L. Fan) "On the parametric representation of quasi-conformal mappings," Sci. Sinica 11 (1962), 149-162.
"Measures on functional spaces," Jour. Fudan Univ. 7 (1962), 121-131, 8 (1965), 261-262, Acta Sci. Sinica 12 (1963), 479-494.
(with Z. Wu and W. Zhang) "On the semi-group of unitary operators on the indefmite metric space and the conditional positive-definite generalized functions," Selected Works on Science in Shanghai 1 (1960), 28-45.
(with L. Fan) "On the parametric representation of quasi-conformal mappings and its applications," Selected Works of Science in Shanghai 1 (1960), 66-99.
(with L. Fan) "On the modulus of quasi-conformal mapping,"Sci. Record, New Series 4 (1960),3 23-328.
(with S. Van) "On the distributions in the dual space of nuclear space," Collected Works on Mathematics of Fudan Univ.(1959), 413-418.
(with Z. Wu and W. Zhang) "On conditionally positive-definite generalized functions of several variables," Collected Works on Mathematics of Fudan University (1959), 437-448.
"On semi-normed rings with involution," (in Russian), Dokl. Akad. Nauk, SSSR 124 (1959), 1223-1225, Izv. Adad. Nauk, SSSr. Ser. Mat. 23 (1959), 509-528.
"Positive functional on algebras," (in Russian), Dokl. Akad. Nauk, SSSR 124 (1959), 1223-1225, Izv. Akad. Nauk, SSS4, Ser. Mat. 23 (1959), 509-528.
"Parametric representation of quasi-conformal mappings," Sci. Record, New Series 3 (1959), 400-407, Jour. Fudan Univ.(1959), 26-44.
(with I.M. Gelfand) "On positively defmite generalized functions," (in Russian), Usp. Math. Nauk, SSSR 151 (1958).
"The method of variation and Loewner's method in the theory of Schlicht functions," Jour. Fudan Univ. 1 (1958), 30-34.
"The minimum of the mean diameters of the Schlicht mappings," Jour. Fudan Univ. 1 (1958), 28-29.
(with K. Zhang) "Some inequalities in the theory of subordination," Acta Math. Sinica 8 (1958), 408-412.
"Ring of analytic functions," Jour. Furlan Univ. 2 (1957), 352-356.
"Typically-real functions on the multiply-connected domains,"Jour. Fudan Univ. 1 (1957), 138-145.
"Some covering properties of convex domains in the theory of conformal mapping," Acta Math. Sinica 7 (1957), 421-432, Sci. Sinica 8 (1958), 816-828.
"On the radius of superiority in subordination," Sci. Record, New Series 1 (1957), 329-333.
"Goluzin's number (3-square root of 5)/2 is the radius of superiority in subordination," Sci. Record, New Series 1 (1957), 219-222.
"A shorter proof of Z. Charizynski's theorem," Prog. Math 2(1956), 714-720.
"An application of the theory of positive quadratic differential form to the product of mapping radii," Acta Math. Sinica 6 (1956), 583-597.
"On the functions univalent in a circular ring," Acta Math. Sinica 6 (1956), 598-618.
"Points exterior to the image domains for functions ofstarlikeness as well as of convexity," Jour. Furlan Univ. 2 (1956), 125-132.
"On the dual quasi-invariant measures," Acta Math. Sinica 6 (1956), 70-78.
The principle of area in the theory of univalent functions I,Jour. Furlan Univ. 2 (1956), 134-145.
"A covering theorem of a starlike domain," Jour. Furlan Univ. 1 (1955), 51-54.
"On the moduli of some classes of analytic functions," Acta Math. Sinica 5 (1955), 439-454.
"The products of mapping radii of non-overlapping domains,"Acta Math. Sinica 5 (1955), 27- 36.
"The principle of area in the theory of univalent functions,"Acta Math. Sinica 3 (1953), 208- 212.
"On the product of mapping radii for a system of non-overlapping domains," Acta. Math. Sinica 3 (1953), 1-7.
"Theorems of distorsion and coefficients of Schlicht functions,"Sci. Record 4 (1951), 351-362.
"On the distorsion of Schlicht function," Sci. Record 4 (1951), 209-212.
"On the coefficients of Schlicht functions," Acta Math. Sinica 1 (1950), 98-107.
Conference Talks
2015: Conference on Functional Analysis, Shanghai, China
2014: International Conference on Analysis, Qongqing, China
2013: International Conference on Modern Analysis, Shanghai, China
2013: Chang Jianggong Research Institute of Mathematics, Hangzhou Normal University, Hangzhou, China
2012: Department of Mathematics, Chongqing University
2012: National Conference on Operator Theory, Chongqing, China
2011: SE Analysis Meeting, Giansville, FL
2009: International Conference on Operator Theory and Operator Algebra, Suzhou, China.
2008: Research Institute of Mathematics, Zhejiang University, China.
2008: Research Institute of Mathematics (Chern Institute), Nankai University, China.
2008: Department of Mathematics, Sandong University (Weihai Campus), China.
2008: Conference on Operator Theory (related to geometry), Quianhuandao, China.
2007: Department of Mathematics, Suzhou University, China.
2005: International Conference on Partial Differential Equations and Its Application to Geometry and Physics, Shanghai, China.
2005: SE Analysis Meeting, Lexington, VA.
2004: Special Session of American Mathematical Society, Nashville, TN
2004: Chinese Functional Analysis Conference, Shanghai.
2004: SE Analysis Meeting, Tuscaloosa, AL
2003: Analysis Seminar, Department of Mathematics, York University, Canada
2003: Seminar in Research Institute of Mathematics, and Colloquium in the Department of Mathematics, Fundan University, Shanghai
2002: Research Institute of Mathematics, Sangdong University, Jijiang, China
2001: Special Session, American Mathematical Society, New Orleans, LA
2000: Departments of mathematics, Zhejiang University, Nanjing University, China
1999: Department of Mathematics, Fudan University, Shanghai
1999: Special Session of American Mathematical Society Annual Meeting, Gainesville, FL
1998: SE Analysis Meeting, Tuscaloosa, AL (March)
1997: Analysis Seminar, Department of Mathematics, York University, CN
1997: SE Analysis Meeting, Gainesville, FL
1996: Special Session, American Mathematical Society, Iowa City, IA
1996: Research Institutes of Mathematics or Departments of Mathematics, Academy Sinica, Tapei and Beijing, National Central University, Taiwan, Normal University of East China, Shanghai, and National Jiao Tong University, Taiwan
1996: Annual Meeting of the American Mathematical Society, Orlando, FL
1995: Canadian Operator Symposium, Waterloo, CN
1995: SE Analysis Meeting, Atlanta, GA
1995: GPOTS, Cincinnati, OH
1995: Annual Meeting of the American Mathematical Society, San Francisco, CA
1995: International Workshop of Operator Theory & its Applications, Regensburg, Germany
1995: Canadian Operator Symposium, Waterloo, CN
1995: SE Conference on Analysis, Atlanta, GA
1995: GPOTS, Cincinnati, OH
1995: Annual Meeting of the American Mathematical Society, San Francisco, CA
1994: GPOTS, NE
1994: Seminar of Operator Theory, SUNY, Buffalo
1994: International Operator Theory Workshop, Banach Center, Polish Academy of Science
1994: SE Analysis Meeting, VA
1994: Summer Research Conference of Multivariable Operator Theory, Seattle, W A Functional Analysis Colloquium, University of California, Berkeley
1993: Departments of Mathematics, Hong Kong Chinese University, Hong Kong University of Science and Technology, Hong Kong University
1992: Special Session of American Mathematical Society, Tuscaloosa. AL
1992: SE Analysis Meeting, Knoxville, TN
1991: Seminar of Operator Theory, SUNY, Buffalo
1991: GPOTS, Austin, TX
1991: Conference of Analysis, Charlotte, NC
1991: Annual Meeting of the American Mathematical Society, San Francisco, CA
1990: Annual Meeting of the American Mathematical Society, Louisville, KY
1990: GPOTS, Albuquerque, NM
1989: Functional Analysis Seminars, SUNY at Buffalo and Stony Brook
1989: GPOTS, Houston, TX
1988: Functional Analysis Seminar, Purdue University
1988: Summer School of Operator Theory & Operator Algebra, New Hampshire
1988: SE Analysis Meeting, VA
1987: Analysis Meeting, Tuscaloosa. AL
1987: Great Plains Operator Theory Symposium (GPOTS), Lawrence, KS
1987: Conference of Functional Analysis, Tempe, AZ
1987: Departments of Mathematics, Purdue University, SUNY at Buffalo, and Indiana University Purdue University at Indianapolis
1987: Wabash Extramural Functional Analysis Seminar, IN
1986: Conference on Operator Theory, Bloomington, IN
1986: International Congress of Mathematics
1986: Southeast (SE) Analysis Meeting, Chapel Hill, NC SE
1985: Lectured in conferences in Berkeley, Santa Barbara, CA, Iowa City and NE
1984: Departments of Mathematics, University of Maryland, University of Florida, Wayne State University, Cleveland State University, Vanderbilt University, San Diego State University
1984: International Colloquium of Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory, France
1983-1985: Fifth International Conference of Mathematical Physics, Switzerland
1983: Departments of Mathematics, University of Notre Dame, State University of Iowa, University of Delaware, University of Houston, Princeton
1982: Conferences of Hannonic Analysis, and Representations of Lie Groups, University Bielfield and Mathematisches Forschungsinstitiit Oberwolfach
1981: 6th International Conference of Mathematical Physics, West Berlin
1981: Department of Mathematics, Universitat Munchen
1980: Departments of Mathematics or Seminars of Functional Analysis and Operator Theory at the University of California, Berkeley, Los Angeles, Los Alamos Scientific Laboratory, Purdue University, Washington University, Yale University, University of Toronto, University of Pennsylvania, University of Maryland, Ohio State University, University of Michigan, Massachusetts Institute of Technology, University of Cincinnati, Kyushu University, and Nagoya University
1980: Two special sessions of American Mathematical Society, Colorado, and Pennsylvania
1979: Departments of Mathematics, Osaka University, University of Osaka Prefecture, Kyoto University and Tokyo University, Japan
Editorships
Editorial Board of the Integral Equation and Operator Theory, 1978-
Editorial Board of the series of monographs of Operator Theory Advances and Applications, 1978-
Editorial Board of Scientia Sinica, 1972-1986
Editorial Board of Kexue Tongbao (a monthly Journal of Science, Academia Sinica), 1972-1986
Deputy Editor of a series of monographs of Contemporary Fundamental Mathematics (published by the press of the Academia Sinica) 1982-1990
Editorial Board of a series of monographs of Contemporary Mathematics (published by the Shanghai Press of Science and Technology) 1982-1990
Deputy Editor of the Journal of Applied Sciences, 1981-1982
Editor of the Chinese Annals of Mathematics, 1978-1996
Grants
6/1985 - 5/1987 NSF Grant #DMS-8502359
6/1987 - 5/1989 NSF Grant #DMS-8700048
6/1989 - 5/1991 NSF Grant #DMS-8901506
6/1991 - 5/1993 NSF Grant #DMS-9101268
6/1994 - 5/1997 NSF Grant #DMS-9400766
10/1998 - 2/1999 NSF Grant #DMS-9970813
10/2007 - 2/2008 NSF Grant #DMS-0800572
Awards
Third Place Chinese National Prize of Natural Sciences, 1982. For "Functional Integration and Spectral Theory of Operators" (with S.Z. Yan).
Fourth Place Chinese National Prize of Natural Sciences, 1982. For "Geometric Theory of Function" (with S.Gung).
Elected as academician of Academia Sinica (Science Academy of China), 1980.
Students
Ph.D. Students
Zhang, Y:L., Theory of the Quasi-invariant Measures on the Locally Non-compact Groups, 1982.
Li, S.K., On the Non-nonnal Operators, 1982.
Tong, Y:S., Some New Results of the Spectral Analysis of Linear Operators on the Indefinite Inner Product Spaces, 1982.
Aluthge, A., Properties of p-hyponormal operators, 1990.
Knisley, J.R., The analytic model of a semi-hyponormal operator with rank one polar difference, 1990.
Shirley, K.L., A scalar-valued analytic model for a class of subnormal operators, 1991.
Fryd; M, Taylor invertibility for commuting operator n-tuples on Hilbert space, 1993.
Burton, D., On hyponormal tuples of commuting operators with fmite rank self-commutators, 1997.
Stewart, S.A., Some families of subnonnal operators with fmite ranak self-commutators, 2001.