Related papers: Some Parseval-Goldstein Type Theorems For Generali…
We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mordell-Weil groups of elliptic curves over number fields.…
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their fundamental classes, in terms of Parseval-Rayleigh…
We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of…
Let $\mathcal{S}\subset \mathcal{L}^2 \subset \mathcal{S}^*$ be the Gel'fand triple over the Bernoulli space, where elements of $\mathcal{S}^*$ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli…
In this paper, the authors gives a new identity for Hadamard fractional integrals. By using of this identity, the authors obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (alpha?;m)-GA-convex…
We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth setting are derived and applications to generalized rotational…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
We present some integral transform that allows to obtain solutions of the generalized Tricomi equation from solutions of a simpler equation. We used in [13,14],[41]-[46] the particular version of this transform in order to investigate in a…
Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, and generalized divided difference. Previous…
In this article we study the existence of pathwise Stieltjes integrals of the form $\int f(X_t)\, dY_t$ for nonrandom, possibly discontinuous, evaluation functions $f$ and H\"older continuous random processes $X$ and $Y$. We discuss a…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…
We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the…
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.
We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…