Multiparameter Eigenvalue Problems: Sturm-Liouville Theory by F.V. Atkinson

Multiparameter Eigenvalue Problems: Sturm-Liouville Theory

F.V. Atkinson and Angelo B. Mingarelli
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“With special attention to the Sturm-Liouville theory, this book discusses the full multiparameter theory as applied to second-order linear equations. It considers the spectral theory of these multiparameter problems in detail for both the regular and singular cases. The text covers eignencurves, the essential spectrum, eigenfunctions, oscillation theorems, the distribution of eigencurves, the limit point, limit circle theory, and more. This text is the culmination of more than two decades of research by F.V. Atkinson, one of the masters in the field, and his successors, who continued his work after he passed away in 2002”—

Publisher Description

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. Atkinsona (TM)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. Atkinsona (TM)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.

Review
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

Author Biography

F.V. Atkinson was a professor emeritus of mathematics at the University of Toronto. A Fellow of the Royal Society of Canada and an Honorary Fellow of the Royal Society of Edinburgh, Dr. Atkinson was awarded the Makdougall-Brisbane Prize of the Royal Society of Edinburgh for his enduring paper on limit-n criteria of integral type. He published more than 100 papers on subjects ranging from the theory of the Riemann zeta function to operator theory. He earned his Ph.D. from the University of Oxford, under the guidance of E.C. Titchmarsh. Angelo B. Mingarelli is a professor of mathematics at Carleton University. He previously taught at the Pennsylvania State University and the University of Ottawa. Dr. Mingarelli has been an NSERC University Research Fellow for many years and has won numerous awards for excellence in teaching. He earned his Ph.D. from the University of Toronto, under the supervision of F.V. Atkinson.

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Multiparameter Eigenvalue Problems: Sturm-Liouville Theory

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