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The Hausdorff moments in statistical mechanics

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journal contribution
posted on 2023-06-08, 18:28 authored by Enrico Scalas, G A Viano
A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or round-off errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(ß) (ß=1/k BT ) is obtained which coincides with a Watson resummation of the high-temperature series for Z(ß).

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Mathematical Physics

ISSN

0022-2488

Publisher

American Institute of Physics

Volume

34

Page range

5781-5800

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-10-03

First Open Access (FOA) Date

2014-10-03

First Compliant Deposit (FCD) Date

2014-10-03

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