Multiparameter Eigenvalue Problems

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.

• 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.

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