Remarks on some dirichlet type results for semibounded Sturm-Liouville operators
β Scribed by Hubert Kalf
- Publisher
- Springer
- Year
- 1974
- Tongue
- English
- Weight
- 438 KB
- Volume
- 210
- Category
- Article
- ISSN
- 0025-5831
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π SIMILAR VOLUMES
In one of his works, M.G. Krein discovered an analogy between polynomials orthogonal on the unit circle and generalized eigenfunctions of certain differential systems. We used some ideas of this paper to obtain new results in spectral analysis of Sturm-Liouville operators.
Let \(\lambda_{n}(q)\) be the \(n\)th eigenvalue of the Sturm-Liouville equation \(y^{\prime \prime}+(\lambda-q(x)) y=0\), \(y(-l / 2)=y(l / 2)=0\). With certain restrictions on the class of functions \(q\) we determine the shapes of the solutions of the extremal problems for the functionals \(\lamb
## Abstract We offer a new proof of a special Tauberian theorem for Fourier type integrals. This Tauberian theorem was already considered by us in the papers [1] and [2]. The idea of our initial proof was simple, but the details were complicated because we used Bochner's definition of generalized F