Analysis & PDE

  • Anal. PDE
  • Volume 8, Number 1 (2015), 183-221.

Criteria for Hankel operators to be sign-definite

Dimitri Yafaev

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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.

Article information

Anal. PDE, Volume 8, Number 1 (2015), 183-221.

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
Secondary: 47B25: Symmetric and selfadjoint operators (unbounded)

Hankel operators convolutions necessary and sufficient conditions for positivity sign function operators of finite rank the Carleman operator and its perturbations


Yafaev, Dimitri. Criteria for Hankel operators to be sign-definite. Anal. PDE 8 (2015), no. 1, 183--221. doi:10.2140/apde.2015.8.183.

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