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Daoxing Xia 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.

Articles

"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. Theory48 (2004) 115-135. PDF
 
"Trace formulas for some operators related to quadrature domains in Riemann surfaces," Integr. Equ. Oper. Theory47(2003) 123-130. PDF
 
(with S.A. Stewart) "A class of subnormal operators with finite rank self-commutators," Integr. Equ. Opera Theory44 (2002) 370-382. PDF
 
(with D. Zheng) "Compact products of Hankel operators,"Integr. Equ. Opera Theory38 (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.

"On pure subnormal operators with finite rank self-commutators and related operator tuples," Integ. Eq. Opera Theory24 (1996), 107-125.

"Generalized cyclic cohomology associated with deformed commutators," Proc. Amer.Math. Soc. 124 (1996), 1743-1753.

"Trace formulas and complete unitary invariants for some k-tuples of commuting operators," Contem. Math. 185 (1995) 367-380.

"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.

"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.

"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.

"Trace formulas for almost commuting operators, cyclic cohomology and subnormal operators," Integr. Equ. Op. Theory. 14 (1991), 276-198. PDF

"Trace formulas for almost unperturbed SchrOdinger pair of operators," Proc. Amer. Math. Soc. 112 (1991), 755-764.

"Principal distribution for almost unpertubed Shrodinger pair of operators," Proc. Amer. Math. Soc. 112 (1991), 745-754.

"On some classes of hypo normal tuples of commuting operators," Oper. Theory: Advances and Applications 48, Birkhiiuser, Verlag, Basel (1990), 423-448.

"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.

(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 group of operators and cyclic one cocyles," Integr. Equ. Oper. Theory. 9 (1986), 570-587. PDF

"Trace formula for almost Lie algebra of operators and cyclic one cocyles," Lecture Notes in Pure and Applied Mathematics107Nonlinear and Convex Analysis (1987) 299-308.

"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. (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 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. (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.

"Spectral mapping of hyponormal or semi-hyponormal operators," Math. Anal. App. 79 (1981), 409-427.

(with S.Li) "On functional transformation of semi-hyponormal operators," Chinese Ann. Math. 1 (1981), 501-504.

(with S.Li) "On the functional transformation of hyponormal operators," Keuxue Tongbao 25 (1980), 625-627.

"On the Toeplitz operator related to the scattering operator of a semi-hyponormal operator," Acta Math. Sci. 1 (1981), 77-82.

(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, 311-315.

"On the scattering operator with indefmite metric,"Mathematical Problems in Theoretical Physics, edited by K. Osterwalder, Springer-Verlag, 1980.

"On the characteristic function of semi-hyponormal operators,"Chinese Ann. Math. 1 (1980), 1-8.

"On the non-normal operators-semi-hyponormal operators,"Acta Sci. Sinica 23 (1980), 700-713.

"On the invariant subspaces of contraction operator," Jour. Fudan Univ. 1 (1979), 1-9.

"On the representation of locally current algebras and group of diffeomorphisms," Acta Sci. Sinica, Special Issue II (1979), 149-160.

"On the commutational relation in the global gauge theory for group U(I)," Jour. Fudan Univ. 2 (1978),8-13.

"On non-normal operators (II)," Acta Math. Sinica 21 (1978), 187-189.

"On the quantization of global gauge fields (I)," Jour. Fudan Univ. 4 (1977), 13-21.

(with S. Van) "On field strengths, sources and gauge potentials of Yang-Mill's field," Kexue Tongbao 22 (1977), 427-430, Jour. Fudan Univ. 1 (1977), 80-89.

"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.

"On the dual quasi-invariant measures," Acta Math. Sinica 6(1956), 70-78.

"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 locally bounded topological algebras," Sci. Sinica 13(1934), 375-390.

"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.

"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 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 conditionally positive-defmite generalized functions," Sci. Sinica 119 (1962), 1147-1168, Acta. Math. Sinica 113 (1961), 193-201.

"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.

(with I.M. Gelfand) "On positively defmite generalized functions," (in Russian), Usp. Math. Nauk, SSSR 151 (1958).

(with L. Fan) "On the parametric representation of quasi-conformal mappings," Sci. Sinica 11 (1962), 149-162.

(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.

"Parametric representation of quasi-conformal mappings," Sci. Record, New Series 3 (1959), 400-407, Jour. Fudan Univ.(1959), 26-44.

"The method of variation and Loewner's method in the theory of Schlicht functions," Jour. Fudan Univ. (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. (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.

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 (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.