Multiparameter Eigenvalue Problems

<p>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 <strong>Multiparameter Eigenvalue Problems: Sturm-Liouville Theory</strong> reflects much of Dr. Atkinson’s final work.</p><p></p><p>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.</p><p></p><p>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. </p>