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Siberian Mathematical Journal

, Volume 44, Issue 4, pp 638–644 | Cite as

On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

  • A. I. Parfyonov
Article

Abstract

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L2,❘g❘ space of eigenfunctions of an indefinite Sturm–Liouville problem u″=λgu 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.

indefinite Sturm–Liouville problem interpolation space Riesz basis property 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. I. Parfyonov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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