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

Banach Center Publications (1996)

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

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topLeinartas, 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

top- [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] 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] B. Y. Sternin and V. E. Shatalov, On some integral transformations of complex-analytic functions, Dokl. Akad. Nauk SSSR 280 (1985), 553-556.
- [4] L. I. Ronkin, Introduction to the Theory of Entire Functions in Several Variables, Nauka, Moscow, 1971. Zbl0225.32001

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