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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 24, Issue 6


Holomorphic extensions associated with series expansions

Enrico De Micheli / Giovanni Alberto Viano
  • Dipartimento di Fisica, Università di Genova, Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Via Dodecaneso, 33, 16146 Genova, Italy
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Published Online: 2012-11-03 | DOI: https://doi.org/10.1515/form.2011.104


We study the holomorphic extension associated with power series, i.e., the analytic continuation from the unit disk to the cut-plane . Analogous results are obtained also in the study of trigonometric series: we establish conditions on the series coefficients which are sufficient to guarantee the series to have a KMS analytic structure. In the case of power series we show the connection between the unique (Carlsonian) interpolation of the coefficients of the series and the Laplace transform of a probability distribution. Finally, we outline a procedure which allows us to obtain a numerical approximation of the jump function across the cut starting from a finite number of power series coefficients. By using the same methodology, the thermal Green functions at real time can be numerically approximated from the knowledge of a finite number of noisy Fourier coefficients in the expansion of the thermal Green functions along the imaginary axis of the complex time plane.

Keywords: Complex and harmonic analysis; analytic continuation; probability and quantum field theory; KMS condition

About the article

Received: 2010-01-15

Revised: 2010-12-14

Published Online: 2012-11-03

Published in Print: 2012-11-01

Citation Information: , Volume 24, Issue 6, Pages 1269–1316, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.104.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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