AutoriDe Micheli Enrico; Giovanni Alberto Viano
AbstractWe study the holomorphic extension associated with power series, i.e., the analytic continuation from the unit disk to the cut-plane \ 1, ). 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.
RivistaForum Mathematicum
Impact factor
Pagina inizio1316
Pagina fine1269
Linee di Ricerca IBFMD.P01.004.001