Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T11:26:34.738Z Has data issue: false hasContentIssue false

On the Spectrum of the Bergman-Hilbert Matrix II

Published online by Cambridge University Press:  20 November 2018

Chandler Davis
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1
Pratibha Ghatage
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study a class of matrices (introduced by T. Kato) with principal homogeneous part, and use Mellin transform of the homogeneous kernel to determine spectral density of the positive infinite matrices.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Choi, M. D., Tricks or treats with the Hilbert Matrix, Amer. Math. Monthly 90 (1983), 301312.Google Scholar
2. Ghatage, P., On the spectrum of the Bergman-Hilbert-matrix, Linear Algebra and Its Applications 97 (1987), 5763.Google Scholar
3. Hardy, G., Littlewood, J., Pólya, G., Inequalities, Cambridge University Press (1934).Google Scholar
4. Kato, T., On positive eigenvectors of positive matrices, Communications on Pure and Applied Mathematics 11 (1958), 573586.Google Scholar
5. Rochberg, R., Decomposition theorems for Bergman spaces and their applications, Operators and function theory, NATO ASI Series C, 153, 225-277.Google Scholar
6. Wilf, H., Finite Sections of Classical Inequalities, Springer-Verlag, New York, 1970.Google Scholar