Multiparameter Eigenvalue Problems

Sturm-Liouville Theory

F.V. Atkinson, Angelo B. Mingarelli

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English

CRC Press Inc
07 December 2010

Number systems; Differential calculus & equations; Applied mathematics; Mathematical physics; Computing: general; Computer science

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.

By: F.V. Atkinson, Angelo B. Mingarelli
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 18mm
Weight: 544g
ISBN: 9781439816226
ISBN 10: 1439816220
Pages: 302
Publication Date: 07 December 2010
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Hardback
Publisher's Status: Active

Preliminaries and Early History. Some Typical Multiparameter Problems. Definiteness Conditions and the Spectrum. Determinants of Functions. Oscillation Theorems. Eigencurves. Oscillation Properties for Other Multiparameter Systems. Distribution of Eigenvalues. The Essential Spectrum. The Completeness of Eigenfunctions. Limit-Circle, Limit-Point Theory. Spectral Functions. Appendix. Bibliography. Index.

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.

Reviews for Multiparameter Eigenvalue Problems: Sturm-Liouville Theory

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