Small eigenvalues of large Hermitian moment matrices

Escribano Iglesias, M. del Carmen and Gonzalo Palomar, Raquel and Torrano Gimenez, Emilio (2011). Small eigenvalues of large Hermitian moment matrices. "Journal of mathematical analysis and applications", v. 374 (n. 2); pp. 470-480. ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2010.07.053.

Description

Title: Small eigenvalues of large Hermitian moment matrices
Author/s:
  • Escribano Iglesias, M. del Carmen
  • Gonzalo Palomar, Raquel
  • Torrano Gimenez, Emilio
Item Type: Article
Título de Revista/Publicación: Journal of mathematical analysis and applications
Date: February 2011
ISSN: 0022-247X
Volume: 374
Subjects:
Freetext Keywords: Complex moment problem; Orthogonal polynomials; Smallest eigenvalue; Measures; Approximation by polynomials
Faculty: Facultad de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We consider an infinite Hermitian positive definite matrix M which is the moment matrix associated with a measure μ with infinite and compact support on the complex plane. We prove that if the polynomials are dense in L2(μ) then the smallest eigenvalue λn of the truncated matrix Mn of M of size (n+1)×(n+1) tends to zero when n tends to infinity. In the case of measures in the closed unit disk we obtain some related results.

More information

Item ID: 8630
DC Identifier: http://oa.upm.es/8630/
OAI Identifier: oai:oa.upm.es:8630
DOI: 10.1016/j.jmaa.2010.07.053
Official URL: http://www.sciencedirect.com/science/journal/0022247X
Deposited by: Memoria Investigacion
Deposited on: 08 Aug 2011 10:01
Last Modified: 20 Apr 2016 17:20
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