Related papers: On the Generalized Quotient Integrals on Homogenou…
We investigate several boundedness properties of function spaces considered as uniform spaces.
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
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…
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
We consider Poisson's equation on the $n$-dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric identities, we integrate this equation to produce the form…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
We give a general expression of spherical functions on $p$-adic homogeneous spaces of $G$, based on data of $G$ and functional equations of spherical functions. Then, we show a unified method to obtain functional equations of spherical…
We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…
We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.