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The Hausdorff moments in statistical mechanics
journal contribution
posted on 2023-06-08, 18:28 authored by Enrico Scalas, G A VianoA 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).
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- Published
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- Published version
Journal
Journal of Mathematical PhysicsISSN
0022-2488Publisher
American Institute of PhysicsExternal DOI
Volume
34Page range
5781-5800Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2014-10-03First Open Access (FOA) Date
2014-10-03First Compliant Deposit (FCD) Date
2014-10-03Usage metrics
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