Continuation of holomorphic solutions to convolution equations in complex domains

Ryuichi Ishimura; Jun-ichi Okada; Yasunori Okada

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 105-115
  • ISSN: 0066-2216

Abstract

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For an analytic functional S on ℂ n , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in ℂ n . We determine the directions in which every solution can be continued analytically, by using the characteristic set.

How to cite

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Ishimura, Ryuichi, Okada, Jun-ichi, and Okada, Yasunori. "Continuation of holomorphic solutions to convolution equations in complex domains." Annales Polonici Mathematici 74.1 (2000): 105-115. <http://eudml.org/doc/208359>.

@article{Ishimura2000,
abstract = {For an analytic functional $S$ on $ℂ^n$, we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in $ℂ^n$. We determine the directions in which every solution can be continued analytically, by using the characteristic set.},
author = {Ishimura, Ryuichi, Okada, Jun-ichi, Okada, Yasunori},
journal = {Annales Polonici Mathematici},
keywords = {convolution equation; analytic continuation; characteristic set; analytic functional},
language = {eng},
number = {1},
pages = {105-115},
title = {Continuation of holomorphic solutions to convolution equations in complex domains},
url = {http://eudml.org/doc/208359},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Ishimura, Ryuichi
AU - Okada, Jun-ichi
AU - Okada, Yasunori
TI - Continuation of holomorphic solutions to convolution equations in complex domains
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 105
EP - 115
AB - For an analytic functional $S$ on $ℂ^n$, we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in $ℂ^n$. We determine the directions in which every solution can be continued analytically, by using the characteristic set.
LA - eng
KW - convolution equation; analytic continuation; characteristic set; analytic functional
UR - http://eudml.org/doc/208359
ER -

References

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  3. [I2] R. Ishimura, The characteristic set for differential-difference equations in real domains, Kyushu J. Math. 53 (1999), 107-114. Zbl0933.35200
  4. [I-O1] R. Ishimura and Y. Okada, The existence and the continuation of holomorphic solutions for convolution equations in tube domains, Bull. Soc. Math. France 122 (1994), 413-433. Zbl0826.35144
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  12. [Ll-G] P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Grundlehren Math. Wiss. 282, Springer, Berlin, 1986. Zbl0583.32001
  13. [Lv] B. Ja. Levin, Distribution of Zeros of Entire Functions, Transl. Math. Monographs, Amer. Math. Soc., Providence, 1964. 
  14. [R] L. I. Ronkin, Functions of Completely Regular Growth, Kluwer, 1992. Zbl0754.32001
  15. [Sé] A. Sébbar, Prolongement des solutions holomorphes de certains opérateurs différentiels d'ordre infini à coefficients constants, in: Séminaire Lelong-Skoda, Lecture Notes in Math. 822, Springer, Berlin, 1980, 199-220. 
  16. [V] A. Vidras, Interpolation and division problems in spaces of entire functions with growth conditions and their applications, Doct. Diss., Univ. of Maryland. Zbl0842.32001
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