List of publications and preprints
Serguei Denissov
(Sergey A. Denisov)
  1. An estimate, uniform on the whole line $R$, 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, p.754-761, (transl. in Diff. Equations, Vol.33, N6, 1998, p.757--764).
  2. 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, p.731--732.
  3. Equiconvergence of a spectral expansion corresponding to a Schrodinger operator with summable potential, with Fourier integral. Differ. Uravn., Vol.34, N8, 1998, p.1043-1048, (transl. in Diff. Equations, 34, (1998), N8, p.1046--1055).
  4.  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, p.158-162, (transl. in Diff. Equations, Vol.36, N2, 2000, p.181--186).
  5. On the growth rate of generalized eigenfunctions of Sturm-Liouville operator. Schnol's Theorem. Mat. Zametki, Vol.67, N1, 2000, p.46-51, (transl. in Math. Notes, Vol.67, N1-2, 2000, p.36--40).
  6. To the question of equiconvergence for one-dimensional Schrodinger operator with uniformly locally summable potential. Funktsional. Anal. i Prilozhen, Vol.34, N3, 2000, p.71--73, (transl. in Funct. Anal. Appl., Vol.34, N3, 2000, p.216-218).
  7. Absolutely continuous spectrum of Schrodinger operators and Fourier transform of the potential. Russian Journal of Math. Physics, Vol.8, N1, 2001, p.14--24.
  8. On the application of some M.G.Krein's results to the spectral analysis of Sturm-Liouville operators. Journal of Mathematical Analysis and Applications, Vol.261, N1, 2001, p.177--191.
  9. To the spectral theory of Krein systems. Integral Equations and Operator Theory, Vol.42, N2, 2002, p.166--173. [dvi] [ps]
  10. Probability measures with reflection coefficients $\{a_n\}\in\ell^4$ and $\{a_{n+1}-a_n\}\in\ell^2$ are Erd\H{o}s measures. Journal of Approximation Theory, Vol.117, N1, 2002, p.42--54. [dvi] [ps]
  11. On the existence of the absolutely continuous component for the measure associated with some orthogonal systems. Communications in Mathematical Physics, Vol.226, 2002, p.205--220. [dvi] [ps]
  12. 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, p.90--104. [dvi] [ps]
  13. On the continuous analog of Rakhmanov's theorem for orthogonal polynomials. J. Funct. Anal., Vol.198, No. 2, 2003, p.465--480. [dvi] [ps]
  14. (With S. Kupin) On singular spectrum of Schrodinger operators with decaying potential, (to appear in Transactions of the AMS, revised version), 23 pages. [dvi] [ps]
  15. (With B. Simon) Zeros of orthogonal polynomials on the real line. J. Approx. Theory, Vol.121, 2003, p.357--364. [dvi] [ps]
  16. On Rakhmanov's Theorem for Jacobi Matrices. Proceedings of the AMS, Vol.132, 2004, p.847--852. [dvi] [ps]
  17. On the existence of wave operators for some Dirac operators with square summable potentials, (to appear in GAFA), 5 pages, [dvi] [ps]
  18. On the absolutely continuous spectrum of Dirac operator, (to appear in Communications in PDE), 21 pages, [ps]
  19. Absolutely continuous spectrum of multidimensional Schrodinger operator, (preprint), 16 pages, [ps]
  20. (With S. Kupin) Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight, (preprint), 20 pages, [ps]
Lecture notes.
  1. Krein systems, (lecture notes of the course given at Caltech in Fall, 2001), the first draft is available upon request.
Some research letters.
  1. Remarks on the constructive description of $H_{ac}$ and $H_{s}$ for Schrodinger operators with slowly decaying potentials, (preprint). [dvi] [ps]
  2. On the absolutely continuous spectrum of one operator, (preliminary version, preprint). [dvi] [ps]