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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 3, Pages 84–88 (Mi faa2869)  

This article is cited in 1 scientific paper (total in 2 paper)

Brief communications

One-Dimensional Schrödinger Operator on the Half-Line: the Differential Equation for Eigenfunctions with Respect to the Spectral Parameter and an Analog of the Freud Equation

V. S. Buslaev, V. Yu. Strazdin

Saint-Petersburg State University

Abstract: It is shown that the eigenfunctions of the Schrödinger operator on the half-line satisfy an explicitly constructed differential equation with respect to the spectral parameter. Such an equation was earlier obtained for orthogonal polynomials. An analog of the Freud equation is found.

Keywords: one-dimensional Schrödinger equation, Freud equation, eigenfunctions of the Schrödinger equation, spectral function

DOI: https://doi.org/10.4213/faa2869

Full text: PDF file (134 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:3, 237–240

Bibliographic databases:

UDC: 517.927, 517.984
Received: 05.02.2007

Citation: V. S. Buslaev, V. Yu. Strazdin, “One-Dimensional Schrödinger Operator on the Half-Line: the Differential Equation for Eigenfunctions with Respect to the Spectral Parameter and an Analog of the Freud Equation”, Funktsional. Anal. i Prilozhen., 41:3 (2007), 84–88; Funct. Anal. Appl., 41:3 (2007), 237–240

Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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\vol 41
\issue 3
\pages 84--88
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Strazdin V.Yu., “Matrichnyi operator Shredingera na poluosi: differentsialnoe uravnenie dlya obobschennykh sobstvennykh funktsii nepreryvnogo spektra otnositelno spektralnogo parametra i analog uravneniya Froida”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 4: Fizika, khimiya, 2009, no. 4, 49–61
    2. V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174  mathnet  crossref  mathscinet  zmath  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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