The uniform over the whole line R estimates of spectral expansions related to the selfadjoint extensions of the Hill operator and of the Schrödinger operator with a bounded and measurable potential
✍ Scribed by I. Antoniou; V.A. Il'in
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 394 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
We consider some properties of the spectral expansions related to selfadjoint extensions of the operator Hu -----u" + q(x)u over the whole line R in the case when q(x) is a continuous periodic function (the Hill operator) and in the case when q(x) is a bounded measurable function. This paper gives a brief description of results obtained in the following directions: the uniform over R estimates of the generalized eigenfunctions, the uniform over R estimates of the spectral function, the uniform over R equiconvergence with the Fourier integral expansion, and the uniform over R rate of convergence for functions from the Sobolev-Liouville classes.