Related papers: Integral transforms defined by a new fractional cl…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
We define and develop a framework to understand functional integrals as countable families of Banach-valued Haar integrals on locally compact topological groups. The definition forgoes the goal of constructing a genuine measure on an…
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…
Within the functional calculi of Bochner-Phillips and Hirsch, we describe the operators of distributed order differentiation and integration as functions of the classical differentiation and integration operators respectively.
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…
In this article we study the basic theoretical properties of Mellin-type fractional integrals, known as generalizations of the Hadamard-type fractional integrals. We give a new approach and version, specifying their semigroup property,…
We characterize all entire functions that transform a weighted Banach spaces of analytic functions $\mathcal{H}^{\infty}_{\mu_1}$ into another space of the same kind $\mathcal{H}^{\infty}_{\mu_2}$ by superposition for very general weights…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…
Fractional differential (and difference) operators play a role in a number of diverse settings: integrable systems, mirror symmetry, Hurwitz numbers, the Bethe ansatz equations. We prove extensions of the three major results on algebras of…
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…
A bounded linear operator between Banach spaces is called {\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous…
In this paper, we have introduced the Prabhakar fractional $q$-integral and $q$-differential operators. We first study the semi-group property of the Prabhakar fractional $q$-integral operator, which allowed us to introduce the…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
The powerful concept of an operator ideal on the class of all Banach spaces makes sense in the real and in the complex case. In both settings we may, for example, consider compact, nuclear, or $2$--summing operators, where the definitions…
We consider and discuss some basic properties of the bicomplex analog of the classical Bargmann space. The explicit expression of the integral operator connecting the complex and bicomplex Bargmann spaces is also given. The corresponding…