On the Cauchy problem in a class of entire functions in several variables

Eugeni Leinartas

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 189-192
  • ISSN: 0137-6934

Abstract

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We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of ℂ n + 1 . The Borel transformation of power series and residue theory are used as the main methods of investigation.

How to cite

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Leinartas, Eugeni. "On the Cauchy problem in a class of entire functions in several variables." Banach Center Publications 33.1 (1996): 189-192. <http://eudml.org/doc/262713>.

@article{Leinartas1996,
abstract = {We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of $ℂ^\{n+1\}$. The Borel transformation of power series and residue theory are used as the main methods of investigation.},
author = {Leinartas, Eugeni},
journal = {Banach Center Publications},
keywords = {integral representation; Cauchy problem; differential equation with constant coefficients; entire functions; Borel transformation; power series; residue theory},
language = {eng},
number = {1},
pages = {189-192},
title = {On the Cauchy problem in a class of entire functions in several variables},
url = {http://eudml.org/doc/262713},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Leinartas, Eugeni
TI - On the Cauchy problem in a class of entire functions in several variables
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 189
EP - 192
AB - We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of $ℂ^{n+1}$. The Borel transformation of power series and residue theory are used as the main methods of investigation.
LA - eng
KW - integral representation; Cauchy problem; differential equation with constant coefficients; entire functions; Borel transformation; power series; residue theory
UR - http://eudml.org/doc/262713
ER -

References

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  1. [1] M. Miyake, Global and local Goursat problems in the class of holomorphic or partially holomorphic functions, J. Differential Equations 39 (1981), 445-463. Zbl0495.35002
  2. [2] J. Persson, On the global and local non-characteristic Cauchy problems when the solutions are holomorphic functions or analytic functionals in space variables, Ark. Mat. 9 (1971), 171-180. Zbl0222.35001
  3. [3] B. Y. Sternin and V. E. Shatalov, On some integral transformations of complex-analytic functions, Dokl. Akad. Nauk SSSR 280 (1985), 553-556. 
  4. [4] L. I. Ronkin, Introduction to the Theory of Entire Functions in Several Variables, Nauka, Moscow, 1971. Zbl0225.32001

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