The inverse Sturm–Liouville problem III
✍ Scribed by Björn E. J. Dahlberg; Eugene Trubowitz
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 384 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0010-3640
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## Abstract The problem of small vibrations of a graph consisting of __n__ smooth inhomogeneous stretched strings joined at the vertex with the pendant ends fixed is reduced to the Sturm–Liouville boundary problem on a star‐shaped graph. The obtained problem occurs also in quantum mechanics. The sp
We consider a Sturm -Liouville operator Lu = -(r(t)u ) +p(t)u, where r is a (strictly) positive continuous function on ]a, b[ and p is locally integrable on ]a, b[ . Let r 1 (t) = t a (1/r) ds and choose any c ∈ ]a, b[ . We are interested in the eigenvalue problem Lu = λm(t)u, u(a) = u(b) = 0, and t