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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 4, Pages 810–819
(Mi smj1215)
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This article is cited in 32 scientific papers (total in 32 papers)
On an embedding criterion for interpolation spaces and application to indefinite spectral problems
A. I. Parfenov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the $L_{2,|g|}$ space of eigenfunctions of an indefinite Sturm–Liouville problem $u''=\lambda gu$ on the interval $(-1,1)$ with the Dirichlet boundary conditions, provided that the function $g(x)$ changes sign at the origin. In particular, the basis property criterion is established for an odd $g(x)$. Some connections with stability in interpolation scales are discussed.
Keywords:
indefinite Sturm–Liouville problem, interpolation space, Riesz basis property.
Received: 05.04.2002
Citation:
A. I. Parfenov, “On an embedding criterion for interpolation spaces and application to indefinite spectral problems”, Sibirsk. Mat. Zh., 44:4 (2003), 810–819; Siberian Math. J., 44:4 (2003), 638–644
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https://www.mathnet.ru/eng/smj1215 https://www.mathnet.ru/eng/smj/v44/i4/p810
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Abstract page: | 373 | Full-text PDF : | 91 | References: | 52 |
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