Related papers: Cauchy Type Integrals of Algebraic Functions

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…

We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the…

As was the case in a previous paper, the differential form x+ydxdy plays the role that the variable z plays in the standard calculus of complex variable. The role of holomorphic functions will now be played by strict harmonic differential…

We show that every operator in $L^{2}$ has an associated measure on a space of functions and prove that it can be used to find solutions to abstract Cauchy problems, including partial differential equations. We find explicit formulas to…

Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…

Special classes of analytic functions, denoting by K and J arc considered in this paper.

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…

Let $\Gamma$ be the unit circle, $A(\Gamma)$ the Wiener algebra of continuous functions whose series of Fourier coefficients are absolutely convergent, and $A^+$ the subalgebra of $A(\Gamma)$ of functions whose negative coefficients are…

In the introduction part of this paper, first of all, the concept of absolute integral sum of complex function is defined, as more general one with respect to the concept of integral as well as of integral sum of "ordinary'' integral…

Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…

Rays are classes of an equivalence relation on a module V over a supertropical semiring. They provide a version of convex geometry, supported by a "supertropical trigonometry" and compatible with quasilinearity, in which the CS-ratio takes…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we develop a global complex functional calculus on graded Lie…

The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex…

The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous…

In this paper we deal with a new class of Clifford algebra valued automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. The forms that we consider are in the kernel of the operator $D \Delta^{k/2}$ for some even $k \in…

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…