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

• Autorzy: Eugeni Leinartas
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 189-192

Daty

wydano

1996

Twórcy

autor

Eugeni Leinartas

• Krasnoyarsk State University, Svobodny 79, 660062 Krasnoyarsk, Russia

Bibliografia

• [1] M. Miyake, Global and local Goursat problems in the class of holomorphic or partially holomorphic functions, J. Differential Equations 39 (1981), 445-463.
• [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.
• [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.