Holomorphic extensions associated with series expansions
-
Enrico De Micheli
and
Giovanni Alberto Viano
Abstract.
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.
© 2012 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
Articles in the same Issue
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
