List of Publications
Sergey Denisov (aka Serguei
Denissov)
- With A. Aptekarev
and M. Yattselev, Strong asymptotics
of multiple orthogonal polynomials for Angelesco
systems. Part I: non-marginal directions, preprint, [pdf].
- Wave packet decomposition
for Schrodinger evolution with rough potential and generic value
of parameter, St. Petersburg Math. J., 37:2, 2025, 28-59 [pdf].
- With R. Bessonov,
Sobolev norms of L^2-solutions to NLS,
Pacific J. Math., Vol. 331-2, 2024, 217-258, [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