Estimates for Green′s Function of the Sturm-Liouville Operator
✍ Scribed by N. Chernyavskaya; L. Shuster
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 321 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0022-0396
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📜 SIMILAR VOLUMES
This is the second part of a study of the inversion for a Sturm-Liouville difference equation. Our main result consists in getting two-sided (sharp by order) estimates for the diagonal value of the Green difference function
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
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.