一般边界条件下Sturm-Liouville算子的Ambarzumyan型定理

Abstract

Abstract:

This paper deals with the inverse eigenvalue problems for the Sturm-Liouville equation on finite interval with general self-adjoint boundary conditions. The authors extend the classical Ambarzumyan's theorem for the Sturm-Liouville equation with Neumann boundary conditions to the general self-adjoint boundary conditions. They prove that if the spectrum is the same as the spectrum belonging to the zero potential and the potential possesses an integral condition, then the potential is actually zero.

Key words: Ambarzumyans theorem, Inverse spectral theory, Eigenvalue asymptotics, Rayleigh quotient

CLC Number:

34A55

YANG Chuan-Fu, YANG Xiao-Ping. Ambarzumyan's Theorems for Sturm-Liouville Operators with General Boundary Conditions[J].Acta mathematica scientia,Series A, 2010, 30(2): 449-455.

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Ambarzumyan's Theorems for Sturm-Liouville Operators with General Boundary Conditions

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