Ganze Funktionen mit einer vorgeschriebenen asymptotischen Entwicklung.
In the earlier paper [Proc. Amer. Math. Soc. 135 (2007)], we studied solutions g: ℕ → ℂ to convolution equations of the form , where are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form (), where is an additive subsemigroup. If X is discrete and a certain solvability criterion is satisfied,...
Definitions, properties, examples and applications of generalized analytic functions introduced by B. Ziemian are presented.
Mathematics Subject Classification: 44A05, 44A35With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.
2000 Mathematics Subject Classification: 35E45In this paper we study generalized Sobolev spaces H^sG of exponential type associated with the Dunkl operators based on the space G of test functions for generalized hyperfunctions and investigate their properties. Moreover, we introduce a class of symbols of exponential type and their associated pseudodifferential operators related to the Dunkl operators, which act naturally on H^sG.