Analytic continuation of Dirichlet series.

Anderson, J. Milne, Khavinson, Dimitry, and Shapiro, Harold S.. "Analytic continuation of Dirichlet series.." Revista Matemática Iberoamericana 11.2 (1995): 453-476. <http://eudml.org/doc/39469>.

@article{Anderson1995,
abstract = {The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ0∞ an ζn2 (where 0 &lt; |a| &lt; 1) is nowhere continuable across \{|ζ| = 1\}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations (...).},
author = {Anderson, J. Milne, Khavinson, Dimitry, Shapiro, Harold S.},
journal = {Revista Matemática Iberoamericana},
keywords = {Series de Dirichlet; Desarrollo en serie de funciones; Discontinuidad; Funciones analíticas; Funciones de variable compleja; quasianalytic classes},
language = {eng},
number = {2},
pages = {453-476},
title = {Analytic continuation of Dirichlet series.},
url = {http://eudml.org/doc/39469},
volume = {11},
year = {1995},
}

TY - JOUR
AU - Anderson, J. Milne
AU - Khavinson, Dimitry
AU - Shapiro, Harold S.
TI - Analytic continuation of Dirichlet series.
JO - Revista Matemática Iberoamericana
PY - 1995
VL - 11
IS - 2
SP - 453
EP - 476
AB - The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ0∞ an ζn2 (where 0 &lt; |a| &lt; 1) is nowhere continuable across {|ζ| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations (...).
LA - eng
KW - Series de Dirichlet; Desarrollo en serie de funciones; Discontinuidad; Funciones analíticas; Funciones de variable compleja; quasianalytic classes
UR - http://eudml.org/doc/39469
ER -