Related papers: Multidimensional vector-valued Laplace transform a…
The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
In this paper our main aim is to develop some basic properties of hyperbolic valued metric spaces. We also establish the hyperbolic version of Banach contraction principle. Further we construct a hyperbolic valued metric on the space of all…
In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of a…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
In this paper we consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form \[L^p(X)\subseteq \gamma(X) \subseteq L^q(X),\] in…
The main contribution of this paper is that every convex function with non-empty relative algebraic interior of its domain is Lipschitz and subdifferentiable in some algebraic sense without any additional topological constraints. The…
We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a space $\mathcal{F}(\Omega,\mathbb{K})$ of scalar-valued…
This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.
Our principal result is the following. Let $X$ and $Y$ be Banach spaces, let $G$ be a locally compact abelian group, and let $K$ be an operator valued kernel defined on $G$ with values in the space of bounded linear operators from $X$ to…
This book pretends to compile the latest advances on vector-valued Banach limits as well as their applications to vector-valued almost convergence.
The Mittag-Leffler type functions arise naturally in the solution of fractional order integral and differential equations, especially in the investigations of the fractional generalization of the kinetic equation. This article introduces a…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
Let $V$ be a finite dimensional real vector space. In the article we construct an isomorphism between the space of smooth translation invariant valuations on convex subsets of $V$ and the space of such valuations (twisted by densities) on…
We study Bohr's theorem for vector valued holomorphic and operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using invariants from local Banach space theory, we show that the associated Bohr radius is…