Funciones valoradas (I).
An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.
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.