Analyticity of the Eigenvalues and Eigenfunctions of an Ordinary Differential Operator with Respect to a Parameter

Details Analyticity of the Eigenvalues and Eigenfunctions of an Ordinary Differential Operator with Respect to a Parameter Analyticity of the Eigenvalues and Eigenfunctions of an Ordinary Differential Operator with Respect to a Parameter

Feb 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974rspsa.336..475s&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 336, Issue 1607, pp. 475-486

Physics

Scientific paper

We present a general theorem, with simple proof, on the analyticity (with respect to a parameter λ of the eigenvalues and eigenfunctions of a linear homogeneous second-order differential operator widehat{H}λ ). The theorem is more general than commonly used ones (Newton 1960) in so far as the boundary conditions may depend explicitly on the parameter λ and eigenvalue E. We discuss analogous theorems, the meaning of the condition (C) required in the theorem, and boundary conditions at infinity. Finally we extend the theorem to cover homogeneous and non-homogeneous linear problems of arbitrary order, and general non-linear eigenvalue problems.

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