A spectral approach to the Kaplansky problem
Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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Irene Rousseau (2001)
Visual Mathematics
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László Székelyhidi (2013)
Banach Center Publications
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The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modules and in close connection with the Levi-Civita functional equation. Further, we present some open problems in this subject.
Benalili, Mohammed, Lansari, Azzedine (2005)
Lobachevskii Journal of Mathematics
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Vidhyanath K. Rao (1989)
Manuscripta mathematica
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Amaury Mouchet (2012)
ESAIM: Proceedings
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For the one-dimensional Schrödinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case.
Rakhmatullina, L.F. (1997)
Memoirs on Differential Equations and Mathematical Physics
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Robert Grone, Peter D. Johnson, Jr. (1982)
Colloquium Mathematicae
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Tosio Kato (1982)
Mathematische Zeitschrift
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Peter D. Johnson, Jr. (1978)
Colloquium Mathematicae
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Echi, Othman, Gargouri, Riyadh (2004)
The New York Journal of Mathematics [electronic only]
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Zagorodnyuk, S. M. (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.