Multiparameter Eigenvalue Problems

Sturm-Liouville Theory

By: F.V. Atkinson, Angelo B. Mingarelli

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Paperback | 5 September 2019 | Edition Number 1

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304 Pages

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23.4 x 15.6 x 1.63

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One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problems: Sturm-Liouville Theory reflects much of Dr. Atkinson's final work.

After covering standard multiparameter problems, the book investigates the conditions for eigenvalues to be real and form a discrete set. It gives results on the determinants of functions, presents oscillation methods for Sturm-Liouville systems and other multiparameter systems, and offers an alternative approach to multiparameter Sturm-Liouville problems in the case of two equations and two parameters. In addition to discussing the distribution of eigenvalues and infinite limit-points of the set of eigenvalues, the text focuses on proofs of the completeness of the eigenfunctions of a multiparameter Sturm-Liouville problem involving finite intervals. It also explores the limit-point, limit-circle classification as well as eigenfunction expansions.

A lasting tribute to Dr. Atkinson's contributions that spanned more than 40 years, this book covers the full multiparameter theory as applied to second-order linear equations. It considers the spectral theory of multiparameter problems in detail for both regular and singular cases.

Industry Reviews

The book reads well and is accessible to everyone with a background in one-parameter Sturm-Liouville theory. The second author is successful in maintaining Atkinson's admirable style of writing.
--Hans W. Volkmer, Mathematical Reviews, Issue 2011k

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