List of Publications

Sergey Denisov (aka Serguei Denissov)

• Wave packet decomposition for Schrodinger evolution with rough potential and generic value of parameter, preprint, [pdf].
• With A. Aptekarev and M. Yattselev, Strong asymptotics of multiple orthogonal polynomials for Angelesco systems. Part I: non-marginal directions, preprint, [pdf].
• With R. Bessonov, Sobolev norms of L^2-solutions to NLS, to appear in Pacific J. Math., [pdf].
• With B. McMahan, K. Rush, A. Smith, A. Thakurta, Improved differential privacy for SGD via optimal private linear operators on adaptive streams, NeurlPS 2022 conference Proc., [pdf].
• With R. Bessonov, Szego condition, scattering, and vibration of Krein strings, Inventiones Mathematicae, Vol. 234, 2023, 291-373, [pdf]. (extended version where Beurling-Malliavin theorem is used to prove Theorem 2.4 is here).
• Spatial asymptotics of Green's function and applications, J. d'Analyse Mathematique, Vol. 148, 2022, N2, 501-522, [pdf].
• With M. Alexis and A. Aptekarev, Continuity of weighted operators, Muckenhoupt A_p weights, and Steklov problem for orthogonal polynomials, Int. Math. Res. Not. (IMRN), N8, 2022, 5935-5972, [pdf].
• With M. Yattselev, Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality, Advances in Mathematics, Vol. 396, 2022, 108114, 79 pp. [pdf].
• With A. Aptekarev and M. Yattselev, Jacobi matrices on trees generated by Angelesco system: asymptotics of coefficients and essential spectrum, J. Spectral Theory, Vol. 11, N4, 2021, 1511-1597, [pdf].
• Subharmonic functions in scattering theory, C. R. Math. Acad. Sci. Paris, Vol. 359, N6, 2021, 757-762, [pdf].
• With R. Bessonov, De Branges canonical systems with finite logarithmic integral, Analysis and PDE, 14-5, 2021, 1509-1556, [pdf].
• With R. Bessonov, Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials, J. Funct. Anal., Vol. 280, N12, 2021, 109002, [pdf].
• With L. Mohamed, Generalizations of Menchov-Rademacher theorem and existence of wave operators in Schrodinger evolution, Canad. J. Math., Vol. 73, N2, 2021, 360-382, [pdf].
• With R. Bessonov, De Branges canonical systems with finite logarithmic integral, Extended abstracts Fall 2019 - spaces of analytic functions: approximation, interpolation, sampling, 37-41, Trends Math. Res. Perspect. CRM Barc., 12, [pdf].
• With R. Bessonov, A new life of the classical Szego formula, Extended abstracts Fall 2019 - spaces of analytic functions: approximation, interpolation, sampling, 31-36, Trends Math. Res. Perspect. CRM Barc., 12, [pdf].
• With A. Aptekarev, M. Yattselev, On spectrum of a class of Jacobi matrices on graph-trees and multiple orthogonal polynomials, Extended abstracts Fall 2019 - spaces of analytic functions: approximation, interpolation, sampling, 17-24, Trends Math. Res. Perspect. CRM Barc., 12, [pdf].
• With A. Aptekarev and M. Yattselev, Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials, Trans. Amer. Math. Soc., Vol. 373, N2, 2020, 875-917, [pdf].
• With R. Bessonov, A spectral Szego theorem on the real line, Advances in Mathematics, Vol. 359, 2020, 106851, 41 pp., [pdf]. 
• With A. Aptekarev and M. Yattselev, Discrete Schrodinger operator on a graph, Angelesco potentials, and their perturbations, Proc. Steklov Inst. Math.,Vol. 311, 2020, 5-13, [link].
• With K. Choi, On the growth of the support of positive vorticity for 2D Euler equation in an infinite cylinder, Comm. Math. Physics, Vol. 367, N3, 2019, 1077-1093, [pdf]. 
• Spatial asymptotics of Green's function for elliptic operators and applications: a.c. spectral type, wave operators for wave equation, Trans. Amer. Math. Soc., Vol. 371, N12, 2019, 8907-8970, [pdf].
• With J. Breuer and L. Eliaz, On the essential spectrum of Schrodinger operators on trees,  Math. Physics, Analysis and Geometry, 2018, 21:33, [pdf].
• The growth of polynomials orthogonal on the unit circle with respect to a weight w that satisfies w,1/w in L^\infty(T), Mat. Sbornik, Vol. 209, N7, 2018, 71-105, [pdf].
• With K. Rush, On Schur parameters in Steklov's problem, J. Approx. Theory, Vol. 215, 2017, 68-91, [pdf].
• With J. Beichman, 2D Euler equation on the strip: stability of a rectangular patch, Comm. Partial Differential Equations, Vol. 42, N1, 2017, 100-120, [pdf].
• With K. Rush, Orthogonal polynomials on the circle for the weight w satisfying conditions w,1/w in BMO(T), Constr. Approx., Vol. 46(2), 2017, 285-303, [pdf].
• Remark on the formula by Rakhmanov and Steklov's conjecture,  J. Approx. Theory, Vol. 205, 2016, 102-113, [pdf].
• With A. Aptekarev and D. Tulyakov, On a problem by Steklov, Journal of AMS, Vol. 29, N4, 2016, 1117-1165, [pdf].
• On the size of the polynomials orthonormal on the unit circle with respect to a measure which is a sum of the Lebesgue measure and  p point masses, Proceedings of the AMS, Vol. 144, N3, 2016, 1029-1039, [pdf].
• The centrally symmetric V-states for active scalar equations. Two-dimensional Euler with cut-off,  Comm. Math. Phys., Vol. 337, N2, 2015, 955-1009, [pdf].
• The sharp corner formation in 2D Euler dynamics of patches: infinite double exponential rate of merging,  Arch. Rational Mech. Anal., Vol. 215, N2, 2015, 675-705, [pdf].
• Double-exponential growth of the vorticity gradient for the two-dimensional Euler equation, Proceedings of the AMS, Vol. 143, N3, 2015, 1199-1210, [pdf].
• With A. Aptekarev and D. Tulyakov, The problem of V. A. Steklov on the growth rate estimates for orthogonal polynomials, Proc. Steklov Inst. Math., Vol. 289, 2015, 83-106, [pdf].
• The Sobolev norms and localization on the Fourier side for solutions to some evolution equations, Comm. Partial Differential Equations, Vol. 39, N3, 2014, 1635-1657, [pdf]. 
• Multidimensional L2 conjecture: a survey, N. Nikolski Festschrift, Proceedings of the conference "Recent trends in modern analysis 2011", Theta Foundation, 2013, 101-113, [pdf].
• With S. Kupin, On the growth of the polynomial entropy integrals for measures in the Szego class, Advances in Mathematics, Vol. 241, 2013, 18-32. [pdf].
• Remark on Ito's diffusion in multidimensional scattering with sign-indefinite potentials, Annales Henri Poincare, Vol. 14, 2013, N4, 699-708. [pdf].
• With S. Kupin, Ito diffusions, modified capacity, and harmonic measure. Applications to Schrodinger operators, Int. Math. Res. Not., Vol. 2012, 2012, 3127-3181, [pdf].
• The generic behavior of solutions to some evolution equations: asymptotics and Sobolev norms, Discrete Contin. Dyn. Syst. A, Vol. 30, N1, 2011, 77-113, [ps].
• Weak asymptotics for Schrodinger evolution, Math. Modeling Natural Phenomena, Vol. 5, N4, 2010, 150-157 (solicited paper in M.S. Birman memorial volume), [ps].
• Wave equation with slowly decaying potential: asymptotics of solution and wave operators, Math. Modeling Natural Phenomena, Vol. 5, N4, 2010, 122-149 (solicited paper in M.S. Birman memorial volume), [ps].
• On a conjecture by Y. Last, J. Approx. Theory, Vol. 158, 2009, N2, 194-213, [ps].
• Infinite superlinear growth of the gradient for the two-dimensional Euler equation, Discrete Contin. Dyn. Syst. A, Vol. 23, N3, 2009, 755-764 [ps].
• Schrodinger operators and associated hyperbolic pencils, J. Funct. Anal., Vol. 254, 2008, 2186-2226 [ps].
• An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics, Comm. Partial Differential Equations, Vol. 33, N2, 2008, 307-319 [ps].
• Wave propagation through sparse potential barriers, Comm. Pure Appl. Math., Vol. LXI, 156-185 (2008), [ps].
• With A. Kiselev, Spectral properties of Schrodinger operators with decaying potentials, B. Simon Festschrift, Proceedings of Symposia in Pure Mathematics, Vol. 76, AMS 2007, [ps].
• On the preservation of the absolutely continuous spectrum for Schrodinger operators, J. Funct. Anal., Vol. 231, 2006, 143-156 [ps].
• With S. Kupin, Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight, J. Approx. Theory, Vol. 139, 2006, 8-28 [ps]. 
• With S. Kupin, On singular spectrum of Schrodinger operators with decaying potential. Trans. Amer. Math. Soc., Vol.357, N4, 2005, 1525-1544 [ps].
• The theory of orthogonal polynomials and some applications, Proceedings of the 11-th congress in Approximation theory, 2004, Gatlinburg, (2005), Nashboro Press, 151-174.
• Absolutely continuous spectrum of multidimensional Schrodinger operator, Int. Math. Res. Not., N74, 2004, 3963-3982 [ps].
• With S. Kupin, Orthogonal polynomials and a generalized Szego condition. C. R. Math. Acad. Sci. Paris, Vol.339, N4, 2004, 241-244 [pdf].
• The absolutely continuous spectrum of Dirac operator. Comm. Partial Differential Equations, Vol.29, N9-10, 2004, 1403-1428 [ps].
• On the existence of wave operators for some Dirac operators with square summable potentials. Geom. Funct. Anal., Vol.14, N3, 2004, 529-534 [ps].
• On Rakhmanov's Theorem for Jacobi Matrices. Proceedings of the AMS, Vol.132, 2004, 847-852 [ps].
• With B. Simon, Zeros of orthogonal polynomials on the real line. J. Approx. Theory, Vol.121, 2003, 357-364 [ps].
• On the continuous analog of Rakhmanov's theorem for orthogonal polynomials. J. Funct. Anal., Vol.198, N2, 2003, 465-480 [ps].
• On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm-Liouville operators with square summable potential. J. Differential Equations, Vol.191, 2003, 90-104.
• On the existence of the absolutely continuous component for the measure associated with some orthogonal systems. Comm. Math. Phys., Vol.226, 2002, 205-220.
• Probability measures with reflection coefficients a_n from l^4 and a_{n+1}-a_n from l^2 are Erdos measures. J. Approx. Theory, Vol.117, N1, 2002, 42-54.
• To the spectral theory of Krein systems. Integral Equations and Operator Theory, Vol.42, N2, 2002, 166-173.
• On the application of some M.G.Krein's results to the spectral analysis of Sturm-Liouville operators. J. Math. Anal. Appl., Vol.261, N1, 2001, 177-191.
• Absolutely continuous spectrum of Schrodinger operators and Fourier transform of the potential. Russian Journal of Math. Physics, Vol.8, N1, 2001, 14-24.
• To the question of equiconvergence for one-dimensional Schrodinger operator with uniformly locally summable potential. Funktsional. Anal. i Prilozhen, Vol.34, N3, 2000, 71-73, (transl. in Funct. Anal. Appl., Vol.34, N3, 2000, 216-218).
• On the growth rate of generalized eigenfunctions of Sturm-Liouville operator. Schnol's Theorem. Mat. Zametki, Vol.67, N1, 2000, 46-51, (transl. in Math. Notes, Vol.67, N1-2, 2000, 36-40).
• Estimate in L^2(R) norm for the speed of equiconvergence with Fourier integral of spectral resolution that corresponds to the Schrodinger operator with L^1(R) potential. Differ. Uravn., Vol.36, N2, 2000, 158-162, (transl. in Diff. Equations, Vol.36, N2, 2000, 181-186).
• Equiconvergence of a spectral expansion corresponding to a Schrodinger operator with summable potential, with Fourier integral. Differ. Uravn., Vol.34, N8, 1998, 1043-1048, (transl. in Diff. Equations, 34, (1998), N8, 1046-1055).
• Equiconvergence of a spectral expansion corresponding to a Schrodinger operator with a potential in the class L^1(R), with Fourier integral. Dokl. Acad. Nauk, Matematika, Vol.356, N6, 1997, 731-732.
• An estimate, uniform on the whole line, for the rate of convergence of a spectral expansion corresponding to the Schrodinger operator with a potential from the Kato class. Differ. Uravn., Vol.33, N6, 1997, 754-761, (transl. in Diff. Equations, Vol.33, N6, 1998, 757-764).

Lecture notes: Continuous Analogs of Polynomials Orthogonal on the Unit Circle. Krein Systems, Int. Math. Res. Surveys, Vol. 2006 (2006), [ps]

This research was partially supported by NSF Grant DMS-0500177, NSF Grant DMS-0758239, NSF Grant DMS-1067413, NSF FRG Grant DMS-1159133, NSF Grant DMS-1464479, NSF Grant DMS-1764245, NSF Grant DMS-2054465 and by Alfred P. Sloan Research Fellowship