M.Sc. in mathematics, 1982, Leningrad State University
Ph.D. in mathematics, 1985, Leningrad State University,
1986--1989 Branch of Moscow Aviation Institute (MAI) at the Leninsk
(Baikhonoor), assistant professor
1989--1991 Leningrad University, Laboratory of Theoretical
Cybernetics, Researcher
1991--1992 Michigan State University, Dept. of Mathematics,
visiting assistant professor
1992--1994 Michigan State University, Dept. of Mathematics,
assistant professor
1994--1998 Michigan State University, Dept. of Mathematics, associate professor
1998--1999 Michigan State University, Dept. of
Mathematics, professor
Fall 1998 MIT, Dept. of Electrical Engineering and Computer
Science, visiting professor
2000--2001 Brown University, Department of Mathematics,
associate professor
2001--... Brown University, Department of Mathematics,
professor
Kakaroumpas, S.; Treil, S.
"Small step'' remodeling and counterexamples for weighted estimates with arbitrarily "smooth'' weights." Adv. Math., vol. 376, 2021, pp. 52pp.
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Liaw, Constanze, Martin, Robert T.W., Treil, Sergei. "Matrix-valued Aleksandrov–Clark measures and Carathéodory angular derivatives." Journal of Functional Analysis, vol. 280, no. 3, 2021, pp. 108830. |
Liaw, Constanze, Treil, Sergei, Volberg, Alexander. "Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations." International Mathematics Research Notices, 2020. |
Liaw, Constanze, Treil, Sergei. "Matrix measures and finite rank perturbations of self-adjoint operators." Journal of Spectral Theory, vol. 10, no. 4, 2020, pp. 1173-1210. |
Liaw, Constanze, Treil, Sergei. "General Clark model for finite-rank perturbations." Analysis & PDE, vol. 12, no. 2, 2019, pp. 449-492. |
Domelevo, K., Ivanisvili, P., Petermichl, S., Treil, S., Volberg, A. "On the failure of lower square function estimates in the non-homogeneous weighted setting." Mathematische Annalen, vol. 374, no. 3-4, 2019, pp. 1923-1952. |
Ivanisvili, Paata, Treil, Sergei. "Superexponential estimates and weighted lower bounds for the square function." Transactions of the American Mathematical Society, vol. 372, no. 2, 2019, pp. 1139-1157. |
Bickel, Kelly, Culiuc, Amalia, Treil, Sergei, Wick, Brett D. "Two weight estimates with matrix measures for well localized operators." Transactions of the American Mathematical Society, vol. 371, no. 9, 2019, pp. 6213-6240. |
Lai, Jingguo; Treil, Sergei. "Two weight Lp estimates for paraproducts in non-homogeneous settings." J. Funct. Anal., vol. 275, no. 1, 2018, pp. 45–72. |
Nazarov, Fedor; Petermichl, Stefanie; Treil, Sergei; Volberg, Alexander. "Convex body domination and weighted estimates with matrix weights." Advances in Mathematics, vol. 318, 2017, pp. 279–306. |
Liaw, Constanze; Treil, Sergei.
"Singular integrals, rank one perturbations and Clark model in general situation. in: Harmonic analysis, partial differential equations, Banach spaces, and operator theory. Vol. 2, 85–132, Assoc. Women Math. Ser., 5, Springer, Cham, 2017." Harmonic analysis, partial differential equations, Banach spaces, and operator theory. Vol. 2, 85–132, Assoc. Women Math. Ser., 5, Springer, Cham, 2017., Springer, 2017.
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Culiuc, Amalia, Treil, Sergei. "The Carleson Embedding Theorem with Matrix Weights." International Mathematics Research Notices, vol. 2019, no. 11, 2017, pp. 3301-3312. |
Liaw, Constanze; Treil, Sergei. "Clark model in the general situation." J. Anal. Math. , vol. 130, 2016, pp. 287–328. |
Treil, Sergei; Volberg, Alexander. "Entropy conditions in two weight inequalities for singular integral operators." Adv. Math., vol. 301, 2016, pp. 499–548. |
Treil, S. "A remark on the reproducing kernel thesis for Hankel operators." St. Petersburg Math. J., vol. 26, no. 3, 2015, pp. 479-485. |
Thiele, Christoph; Treil, Sergei; Volberg, Alexander. "Weighted martingale multipliers in the non-homogeneous setting and outer measure spaces. ." Advances in Mathematics, vol. 285, 2015, pp. 1155–1188. |
Douglas, Ronald G., Krantz, Steven G., Sawyer, Eric T., Treil, Sergei, Wicks, Brett D. "A History of the Corona Problem." Fields Institute Communications, 2014, pp. 1-29. |
Treil, Sergei. "A Remark on Two Weight Estimates for Positive Dyadic Operators." Operator-Related Function Theory and Time-Frequency Analysis, 2014, pp. 185-195. |
Treil, Sergei, Wick, Brett D. "Corona Solutions Depending Smoothly on Corona Data." Fields Institute Communications, 2014, pp. 201-209. |
Hytönen, Tuomas, Pérez, Carlos, Treil, Sergei, Volberg, Alexander. "Sharp weighted estimates for dyadic shifts and the A2 conjecture." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2014, no. 687, 2014. |
Nazarov, Fedor, Reznikov, Alexander, Treil, Sergei, Volberg, ALexander. "A Bellman function proof of the L 2 bump conjecture." JAMA, vol. 121, no. 1, 2013, pp. 255-277. |
Treil, Sergei. "Commutators, paraproducts and BMO in non-homogeneous martingale settings." Revista Matemática Iberoamericana, vol. 29, no. 4, 2013, pp. 1325-1372. |
Liaw, Constanze, Treil, Sergei. "Regularizations of general singular integral operators." Revista Matemática Iberoamericana, vol. 29, no. 1, 2013, pp. 53-74. |
Treil, Sergei.
"Sharp A2 estimates of Haar shifts via Bellman function." Theta Ser. Adv. Math, vol. 16, 2013, pp. 187–208.
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Douglas, R. G., Kwon, H.-K., Treil, S. "Similarity of n-hypercontractions and backward Bergman shifts." Journal of the London Mathematical Society, vol. 88, no. 3, 2013, pp. 637-648. |
Pipher, Jill, Treil, Sergei. "Weak-star convergence in multiparameter Hardy spaces." Proceedings of the American Mathematical Society, vol. 139, no. 04, 2011, pp. 1445-1445. |
Dragicevic, O., Treil, S., Volberg, A. "A Theorem about Three Quadratic Forms." International Mathematics Research Notices, 2010. |
Kwon, Hyun-Kyoung, Treil, Sergei. "Curvature Condition for Non-contractions Does not Imply Similarity to the Backward Shift." Integral Equations and Operator Theory, vol. 66, no. 4, 2010, pp. 529-538. |
Liaw, Constanze, Treil, Sergei. "Rank one perturbations and singular integral operators." Journal of Functional Analysis, vol. 257, no. 6, 2009, pp. 1947-1975. |
Kwon, H.-K., Treil, S. "Similarity of operators and geometry of eigenvector bundles." Publicacions Matemàtiques, vol. 53, 2009, pp. 417-438. |
Treil, Sergei, Wick, Brett D. "Analytic projections, Corona problem and geometry of holomorphic vector bundles." J. Amer. Math. Soc., vol. 22, no. 1, 2008, pp. 55-76. |
Nazarov, F., Treil, S., Volberg, A. "Two weight inequalities for individual Haar multipliers and other well localized operators." Mathematical Research Letters, vol. 15, no. 3, 2008, pp. 583-597. |
Petermichl, Stefanie; Treil, Sergei; Wick, Brett D.
"Carleson potentials and the reproducing kernel thesis for embedding theorems." Illinois J. Math, vol. 51, no. 4, 2007, pp. 547–559.
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Sasane, Amol, Treil, Sergei. "Estimates in corona theorems for some subalgebras of H ∞." Arkiv för Matematik, vol. 45, no. 2, 2007, pp. 351-380. |
Lauzon, Michael, Treil, Sergei. "Scalar and vector Muckenhoupt weights." Indiana Univ. Math. J., vol. 56, no. 4, 2007, pp. 1989-2015. |
Treil, Sergei. "The problem of ideals of H∞: Beyond the exponent 3/2." Journal of Functional Analysis, vol. 253, no. 1, 2007, pp. 220-240. |
Peller, V. V., Treil, S. R. "Approximation by analytic operator functions. Factorizations and very badly approximable functions." St. Petersburg Mathematical Journal, vol. 17, no. 3, 2006, pp. 493-510. |
Treil, Sergei, Wick, Brett D. "The matrix-valued Hp corona problem in the disk and polydisk." Journal of Functional Analysis, vol. 226, no. 1, 2005, pp. 138-172. |
Peller, V. V., Treil, S. R. "Very badly approximable matrix functions." Selecta Mathematica, vol. 11, no. 1, 2005, pp. 127-154. |
Treil, Sergei. "An operator corona theorem." Indiana Univ. Math. J., vol. 53, no. 6, 2004, pp. 1765-1784. |
Lauzon, Michael, Treil, Sergei. "Common complements of two subspaces of a Hilbert space." Journal of Functional Analysis, vol. 212, no. 2, 2004, pp. 500-512. |
Gillespie, T. A.; Pott, S.; Treil, S.; Volberg, A.
"Logarithmic growth for weighted Hilbert transforms and vector Hankel operators." J. Operator Theory, vol. 52, no. 1, 2004, pp. 103–112.
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Treil, S. "Lower Bounds in the Matrix Corona Theorem and the Codimension One Conjecture." Geom. funct. anal., vol. 14, no. 5, 2004, pp. 1118-1133. |
Nazarov, F., Treil, S., Volberg, A. "The Tb-theorem on non-homogeneous spaces." Acta Mathematica, vol. 190, no. 2, 2003, pp. 151-239. |
Nazarov, F., Treil, S., Volberg, A. "Accretive system Tb-theorems on nonhomogeneous spaces." Duke Mathematical Journal, vol. 113, no. 2, 2002. |
Martínez-Avendaño, R. A.; Treil, S. R.
"An inverse spectral problem for Hankel operators." J. Operator Theory, vol. 48, no. 1, 2002, pp. 83-93.
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Treil, S. "Estimates in the corona theorem and ideals ofH ∞ : A problem of T. Wolff." Journal d'Analyse Mathématique, vol. 87, no. 1, 2002, pp. 481-495. |
Nikolski, Nikolai, Treil, Sergei. "Linear resolvent growth of rank one perturbation of a unitary operator does not imply its similarity to a normal operator." Journal d'Analyse Mathématique, vol. 87, no. 1, 2002, pp. 415-431. |
Nazarov, F., Pisier, G., Treil, S., Volberg, A. "Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2002, no. 542, 2002. |
Nazarov, F.; Treil, S.; Volberg, A.
"Bellman function in stochastic control and harmonic analysis." Oper. Theory Adv. Appl., vol. 129, 2001, pp. 393–423.
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Kupin, S.; Treil, S.
"Linear resolvent growth of a weak contraction does not imply its similarity to a normal operator." Illinois J. Math., vol. 45, no. 1, 2001, pp. 229–242.
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GILLESPIE, T. A., POTT, S., TREIL, S., VOLBERG, A. "LOGARITHMIC GROWTH FOR MATRIX MARTINGALE TRANSFORMS." Journal of the London Mathematical Society, vol. 64, no. 3, 2001, pp. 624-636. |
Gillespi, T. A.; Pott, S.; Treilʹ, S.; Volʹberg, A.
"The transfer method in estimates for vector Hankel operators." St. Petersburg Math. J., vol. 12, no. 6, 2001, pp. 1013–1024.
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Hukovic, S.; Treil, S.; Volberg, A.
"The Bellman functions and sharp weighted inequalities for square functions." Oper. Theory Adv. Appl., vol. 113, 2000, pp. 97–113.
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Treil, S., Volberg, A. "Completely regular multivariate stationary processes and the Muckenhoupt condition." Pacific Journal of Mathematics, vol. 190, no. 2, 1999, pp. 361-382. |
Nazarov, F., Treil, S., Volberg, A. "The Bellman functions and two-weight inequalities for Haar multipliers." Journal of the American Mathematical Society, vol. 12, no. 4, 1999, pp. 909-928. |
Nazarov, F.; Treil, S.; Volberg, A.
"Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces." Internat. Math. Res. Notices, vol. 9, 1998, pp. 463–487.
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Peller, V.V., Treil, S.R. "Approximation by Analytic Matrix Functions: The Four Block Problem." Journal of Functional Analysis, vol. 148, no. 1, 1997, pp. 191-228. |
Nazarov, F.; Treil, S.; Volberg, A.
"Cauchy integral and Calderón-Zygmund operators on nonhomogeneous spaces." Internat. Math. Res. Notices, no. 15, 1997, pp. 703–726.
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Treil, Sergei, Volberg, Alexander. "Continuous frame decomposition and a vector Hunt-Muckenhoupt-Wheeden theorem." Arkiv för Matematik, vol. 35, no. 2, 1997, pp. 363-386. |
Nazarov, Fedor, Treil, Serguei, Volberg, Alexander. "Counterexample to the infinite dimensional carleson embedding theorem." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, vol. 325, no. 4, 1997, pp. 383-388. |
Treil, Sergei, Volberg, Alexander, Zheng, Dechao. "Hilbert transform, Toeplitz operators and Hankel operators, and invariant A_infty weights." Revista Matemática Iberoamericana, 1997, pp. 319-360. |
Treil, Sergei. "Unconditional bases of invariant subspaces of a contraction with finite defects." Indiana University Mathematics Journal, vol. 46, no. 4, 1997, pp. 0-0. |
Treil, S, Volberg, A. "Wavelets and the Angle between Past and Future." Journal of Functional Analysis, vol. 143, no. 2, 1997, pp. 269-308. |
Nazarov, Fedor; Treil, Sergei.
"The weighted norm inequalities for Hilbert transform are now trivial." C. R. Acad. Sci. Paris Sér. I Math. , vol. 323, no. 7, 1996, pp. 717–722.
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Treil, S. "On Superoptimal Approximation by Analytic and Meromorphic Matrix-Valued Functions." Journal of Functional Analysis, vol. 131, no. 2, 1995, pp. 386-414. |
Peller, V. V., Treil, S. R. "Superoptimal singular values and indices of infinite matrix functions." Indiana University Mathematics Journal, vol. 44, no. 1, 1995, pp. 0-0. |
Megretskii, A. V., Peller, V. V., Treil, S. R. "The inverse spectral problem for self-adjoint Hankel operators." Acta Mathematica, vol. 174, no. 2, 1995, pp. 241-309. |
Treil, S. "A counterexample on continuous coprime factors." IEEE Transactions on Automatic Control, vol. 39, no. 6, 1994, pp. 1262-1263. |
Treil, Sergei; Volberg, Alexander.
"A fixed point approach to Nehari's problem and its applications." Oper. Theory Adv. Appl., vol. 71, 1994, pp. 165–186.
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Megretskii, Alexander M.; Peller, Vladimir V.; Treil, Serguei R.
"Le problème inverse pour les opérateurs de Hankel autoadjoints. (French) [The inverse problem for selfadjoint Hankel operators]." C. R. Acad. Sci. Paris Sér. I Math. , vol. 317, no. 4, 1993, pp. 343–346.
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Megretsky, A.; Treil, S.
"Power distribution inequalities in optimization and robustness of uncertain systems." J. Math. Systems Estim. Control, vol. 3, no. 3, 1993, pp. 301–319.
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Treil, S. "The stable rank of the algebra H∞ equals 1." Journal of Functional Analysis, vol. 109, no. 1, 1992, pp. 130-154. |
Treilʹ, S. R.
"An inverse spectral problem for the modulus of the Hankel operator, and balanced realizations." Leningrad Math. J., vol. 2, no. 2, 1991, pp. 353–375.
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Treilʹ, S. R.
"Hankel operators, embedding theorems and bases of co-invariant subspaces of the multiple shift operator." Leningrad Math. J., vol. 1, no. 6, 1990, pp. 1515–1548.
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Vasyunin, V. I.; Treilʹ, S. R.
"The inverse spectral problem for the modulus of a Hankel operator." Leningrad Math. J., vol. 1, no. 4, 1990, pp. 859–870.
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Treilʹ, S. R.
"Angles between co-invariant subspaces, and the operator corona problem. The Szőkefalvi-Nagy problem." Soviet Math. Dokl., vol. 38, no. 2, 1989, pp. 394–399.
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Treil’, S. R. "Geometric Methods in Spectral Theory of Vector-Valued Functions: Some Recent Results." Toeplitz Operators and Spectral Function Theory, vol. 42, 1989, pp. 209-280. |
Treilʹ, S. R.
"The resolvent of a Toeplitz operator can grow arbitrarily fast." J. Soviet Math., vol. 44, no. 6, 1989, pp. 868–869.
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Volʹberg, A. L.; Treilʹ, S. R.
"Embedding theorems for invariant subspaces of the inverse shift operator." J. Soviet Math., vol. 42, no. 2, 1988, pp. 1562–1572.
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Treilʹ, S. R.
"Extreme points of the unit ball in the Hardy operator space H∞(E→E∗)." J. Soviet Math., vol. 42, no. 2, 1988, pp. 1653–1656.
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Treilʹ, S. R.
"Invertibility of a Toeplitz operator does not imply its invertibility by the projection method. (Russian)." Dokl. Akad. Nauk SSSR, vol. 292, no. 3, 1987, pp. 563–567.
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Treilʹ, S. R.
"A spatially compact system of eigenvectors forms a Riesz basis if it is uniformly minimal. (Russian)." Dokl. Akad. Nauk SSSR, vol. 288, no. 2, 1986, pp. 308–312.
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Treilʹ, S. R.
"A vector version of the Adamyan-Arov-Kreĭn theorem. (Russian)." Funktsional. Anal. i Prilozhen., vol. 20, no. 1, 1986, pp. 85–86.
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Treilʹ, S. R.
"Moduli of Hankel operators and the V. V. Peller-S. Kh. Khrushchëv problem. (Russian)." Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol. 141, 1985, pp. 39-55.
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Treilʹ, S. R.
"Moduli of Hankel operators and the V. V. Peller-S. V. Khrushchëv problem. (Russian)." Dokl. Akad. Nauk SSSR, vol. 283, no. 5, 1985, pp. 1095–1099.
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Treilʹ, S. R.
"The Adamyan-Arov-Kreĭn theorem: a vector version. (Russian)." Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol. 141, 1985, pp. 56–71.
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Treilʹ, S. R.
"An operator approach to weighted estimates of singular integrals. (Russian)." Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol. 135, 1984, pp. 150–174.
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Treil, S. R.
"The geometric approach to weight estimates of the Hilbert transform. (Russian)." Funktsional. Anal. i Prilozhen., vol. 17, no. 4, 1983, pp. 90-91.
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My research interests lie in the intersection of operator theory, complex analysis and harmonic analysis. Many problems I was working on have their origin in applications, such as Control Theory (H-infinity control, etc.), stationary random processes, signal processing, and wavelets.
Of particular interest are Hankel and Toeplitz operators, functional models of operators (Sz.-Nagy--Foias and DeBranges--Rovnyak models), spectral decompositions of operators, and spectral theory of matrix- and operator-valued functions.
Another area of interests involves Corona Problem and interplay between operator theory and complex geometry.
Most recent research projects involve weighted norm inequalities for singular integral operators, matrix A_p weights, wavelet and frame decompositions, Calderon--Zygmund operators on non-homogeneous spaces and analytic capacity. Spectral theory and perturbation theory are also topics of my recent research: methods of advanced harmonic analysis proved to be very usefult there.
2019--2022: NSF grant DMS-1856719: Collaborative research: Weighted estimates with
matrix weights and non-homogeneous harmonic analysis (joint with F. Nazarov and A. Volberg).
2016--2019: NSF grant DMS-1600139: Collaborative Research: Calderon--Zygmund Operators in
Highly Irregular Environment and Applications (joint with F. Nazarov and A. Volberg).
2013--2016: NSF grant DMS-1301579: Collaborative Research: Universality phenomena and
some hard problems of non-homogeneous Harmonic Analysis (joint with F. Nazarov and A. Volberg).
2008--2013: NSF grant DMS-0800876: Collaborative Research: Bellman function, Harmonic Analysis
and Operator Theory (joint with F. Nazarov and A. Volberg).
2005--2008: NSF grant DMS-0501065: Collaborative research: Non-homogeneous harmonic
analysis, two weight estimates and spectral problems (joint with F. Nazarov and A. Volberg).
2002--2005: NSF grant DMS-0200584: Collaborative Research: Multidimensional and
Non-Homogeneous Harmonic Analysis: Bellman Functions, Perturbations of Normal Operators and Two
Weight Estimates of Singular Integrals (joint with F. Nazarov and A. Volberg).
1999--2002: NSF grant DMS-9970395: Calderon-Zygmund Operators in Non-Classical Situations:
Weighted Norm Inequalities with Matrix Weights, Operators on Non-Homogeneous Spaces and Analytic
Capacity (joint with F. Nazarov and A. Volberg).
1996--1999: NSF grant DMS-9622936: An Operator Approach to Problems in Analysis and
Probability: Matrix Muckenhoupt Weights, Hankel and Toeplitz Operators, Singular Integrals and the
Angle between Past and Future (joint with A. Volberg).
1993--1996: NSF grant DMS-9304011: Hankel Operators and Their Applications (joint with V. Peller).
Year | Degree | Institution |
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1985 | PhD | Leningrad State University |
1982 | MS | Leningrad State University |
MATH 0520 - Linear Algebra |
MATH 0540 - Honors Linear Algebra |
MATH 1130 - Functions of Several Variables |
MATH 1140 - Functions Of Several Variables |
MATH 2210 - Real Function Theory |
MATH 2220 - Real Function Theory |
MATH 2250 - Complex Function Theory |
MATH 2260 - Complex Function Theory |