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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
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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

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