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arXiv · 1602.02021

Holomorphic extensions associated with series expansions

Enrico De Micheli·Giovanni Alberto Viano
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Abstract

We study the holomorphic extension associated with power series, i.e., the analytic continuation from the unit disk to the cut-plane $\mathbb{C} \setminus [1,+\infty)$. 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.

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Enrico De Micheli, Giovanni Alberto Viano. 2016-02-05. Holomorphic extensions associated with series expansions. https://doi.org/10.1515/form.2011.104

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