Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T09:56:25.382Z Has data issue: false hasContentIssue false
  • English
  • Français

EIGENVALUES OF TOTALLY POSITIVE INTEGRAL OPERATORS

Published online by Cambridge University Press:  01 March 1997

S. P. EVESON
S. P. EVESON
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
Get access

Abstract

It is known [10, 11] that if T is an integral operator with an extended totally positive kernel, then T has a countably infinite family of simple, positive eigenvalues. We prove a similar result for a rather larger class of kernels and, writing the eigenvalues of T in decreasing order as (λn)n∈IN, we use results obtained in [4] and [5] to give a formula for the ratio λn+1/ lambda;n analogous to that given in [3] for the case of a strictly totally positive matrix, and to the spectral radius formula

formula here

This may be regarded as a generalisation of inequalities due to Hopf [8, 9].

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 216 - 222
Copyright
© The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)