Related papers: Generalized Integral Operators and Applications
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
In this article, a theory of generalized oscillatory integrals (OIs) is developed whose phase functions as well as amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs)…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are eigenfunctions of the Bessel, resp. Gegenbauer operators.…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
In this paper we explore the notion of inner function in a broader context of operator theory.
Given an automorphism and an anti-automorphism of a semigroup of a Geometric Algebra, then for each element of the semigroup a (generalized) projection operator exists that is defined on the entire Geometric Algebra. A single fundamental…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…