Multiparameter Eigenvalue Problems: Sturm-Liouville Theory

ISBN-13: 9780367383220 / Angielski / Miękka / 2019 / 301 str.

F. V. Atkinson; Angelo B. Mingarelli

Opis

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 for more than 40 years. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, this book reflects much of Dr. Atkinson’s final work. It covers the full multiparameter theory as applied to second-order linear equations and considers the spectral theory of multiparameter problems in detail for both regular and singular cases. Examples are illustrated using Maple™.

Spis treści

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.

O autorze

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.