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2015 Criteria for Hankel operators to be sign-definite
Dimitri Yafaev
Anal. PDE 8(1): 183-221 (2015). DOI: 10.2140/apde.2015.8.183

Abstract

We show that the total multiplicities of negative and positive spectra of a self-adjoint Hankel operator H in L2(+) with integral kernel h(t) and of the operator of multiplication by the inverse Laplace transform of h(t), the distribution σ(λ), coincide. In particular, ± H 0 if and only if ± σ(λ) 0. To construct σ(λ), we suggest a new method of inversion of the Laplace transform in appropriate classes of distributions. Our approach directly applies to various classes of Hankel operators. For example, for Hankel operators of finite rank, we find an explicit formula for the total numbers of their negative and positive eigenvalues.

Citation

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Dimitri Yafaev. "Criteria for Hankel operators to be sign-definite." Anal. PDE 8 (1) 183 - 221, 2015. https://doi.org/10.2140/apde.2015.8.183

Information

Received: 13 April 2014; Accepted: 26 November 2014; Published: 2015
First available in Project Euclid: 28 November 2017

zbMATH: 1312.47035
MathSciNet: MR3336924
Digital Object Identifier: 10.2140/apde.2015.8.183

Subjects:
Primary: 47A40
Secondary: 47B25

Rights: Copyright © 2015 Mathematical Sciences Publishers

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