INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE

Proceedings of the Edinburgh Mathematical Society

Rostyslav O. Hryniv¹ 

[1] Yaroslav V. Mykytyuk

关键词: Primary 34A55;    Secondary 34B24;    34L05;    34L20;    inverse spectral problems;    Sturm–Liouville operators;    singular potentials;    Sobolev spaces;   

DOI  :  10.1017/S0013091504000859

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $sin[0,1]$. The potential is recovered from two spectra or from one spectrum and the norming constants. Necessary and sufficient conditions for the spectral data to correspond to a potential in $W^{s-1}_2(0,1)$ are established.

【 授权许可】

Unknown