LIST OF PUBLICATIONS
Serguei Denissov (aka Sergey A. Denisov)

Multidimensional L2 conjecture: a survey, preprint, [pdf].

The sharp corner formation in 2D Euler dynamics of patches: infinite double exponential rate of merging, preprint, [pdf].

With S. Kupin, On the growth of the polynomial entropy integrals for measures in the Szego class, preprint, [pdf].

Ito’s diffusion in multidimensional scattering with sign-indefinite potentials, preprint, [ps].

Double-exponential growth of the vorticity gradient for the two-dimensional Euler equation, preprint, [pdf].

With S. Kupin, Ito diffusions, modified capacity, and harmonic measure. Applications to Schrodinger operators, to appear in IMRN, [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, 0156-0185 (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, and by Alfred P. Sloan Research Fellowship