Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator

Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator

The paper is about boundary value problem for polynomial pencil of Sturm‐Liouville operators. Especially, we find all coefficients of the operator by using nodal points (zeros of eigenfunctions). Regularly, we find eigenvalues, nodal points, and nodal lengths by Prüfer substitution. These results ar...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 41; no. 17; pp. 7576 - 7582
Main Authors: Goktas, Sertac, Koyunbakan, Hikmet, Gulsen, Tuba
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30-11-2018
Subjects:
Boundary value problems
Eigenvalues
Eigenvectors
Mathematical analysis
nodal points
Operators (mathematics)
polynomial pencil
Polynomials
Prüfer substitution
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Summary:The paper is about boundary value problem for polynomial pencil of Sturm‐Liouville operators. Especially, we find all coefficients of the operator by using nodal points (zeros of eigenfunctions). Regularly, we find eigenvalues, nodal points, and nodal lengths by Prüfer substitution. These results are used to give a reconstruction formula for all complex functions qd(x), d=0,n−1‾, which are known potentials in the theory. However, method is similar with some papers; our results more general then because of including many potential functions.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5220