Multisummability of iterated integrals

Article type: Research Article

Authors: Balser, W.^; | Tovbis, A.^;

Affiliations: Abt. Mathematik V, Universität Ulm, D-7900 Ulm, Germany | Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel

Note: [] Correspondence to: W. Balser, Abt. Mathematik V, Universität VIm, D-7900 VIm, Germany.

Note: [] Supported by the Israelian Ministry of Science and Technology.

Abstract: Multisummability is a technique of assigning a sum to certain formal power series with zero radius of convergence. In this paper, those functions that occur as such sums are characterized. Furthermore, this result is applied in proving multisummability of iterated integrals; these are integrals which frequently occur, e.g., in proofs of the basic Asymptotic Existence Theorem for linear and nonlinear meromorphic differential equations.

DOI: 10.3233/ASY-1993-7204

Journal: Asymptotic Analysis, vol. 7, no. 2, pp. 121-127, 1993