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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. doi:10.1006/aima.1998.1728.

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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.

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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.
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Issue or Number:1
Record Number:CaltechAUTHORS:20170829-154200373
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80930
Deposited By: Tony Diaz
Deposited On:30 Aug 2017 16:16
Last Modified:15 Nov 2021 19:39

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