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Regularity of the Inversion Problem for the Sturm–Liouville Difference Equation: I. Representation of the Davies–Harrell Type for the Green Difference Function

✍ Scribed by N.A. Chernyavskaya; L.A. Shuster

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
246
Category
Article
ISSN
0022-247X

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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