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Two-Parameter Eigenvalue Problems in Ordinary Differential Equations (Research Notes in Mathematics Series) - Softcover
Synopsis
The aim of this Research Note is to present a comprehensive treatment of some problems arising in the spectral theory of two-parameter systems involving ordinary differential equations. In particular, results are presented concerning the spectrum, the Eigenfunction expansion and the structure of the principal subspaces of a two-parameter system under various definiteness assumptions. Unlike most contemporary works in multiparameter spectral theory, the method used in establishing these results is by an analysis of an associated elliptic boundary value problem, ie the relevant results for the elliptic problems are established, and these results are transformed back to the original problem. Since the treatment of some problems involve the theory of linear separators acting in an indefinite inner space, this work is closely connected with a class of problems undergoing much study today by those working in differential equations and functional analysis. Also included is a treatment of a right definite two-parameter Eigenvalue problem involving complex potentials and this again connects the work with an area of investigation attracting much interest at present.
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