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The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

Simon, Barry (1998) The Classical Moment Problem as a Self-Adjoint Finite Difference Operator. Advances in Mathematics, 137 (1). pp. 82-203. ISSN 0001-8708. https://resolver.caltech.edu/CaltechAUTHORS:20170829-154200373

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Abstract

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Padé approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we obtain new results on the convergence of certain Padé approximants for series of Hamburger.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/aima.1998.1728DOIArticle
http://www.sciencedirect.com/science/article/pii/S0001870898917285PublisherArticle
https://arxiv.org/abs/math-ph/9906008arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 1998 Academic Press. Received 13 November 1997, Accepted 3 January 1998. This material is based upon work supported by the National Science Foundation under Grant DMS-9401491.
Funders:
Funding AgencyGrant Number
NSFDMS-9401491
Issue or Number:1
Record Number:CaltechAUTHORS:20170829-154200373
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170829-154200373
Official Citation:Barry Simon, The Classical Moment Problem as a Self-Adjoint Finite Difference Operator, Advances in Mathematics, Volume 137, Issue 1, 15 July 1998, Pages 82-203, ISSN 0001-8708, https://doi.org/10.1006/aima.1998.1728. (http://www.sciencedirect.com/science/article/pii/S0001870898917285)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80930
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Aug 2017 16:16
Last Modified:03 Oct 2019 18:36

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