相关论文: A residue of complex function in three-dimensional…
The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.
We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Ros\'en. These are constructed through functional calculus…
In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…
Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime $p$. The sum over the distinct residues can sometimes be computed independent of the prime $p$; for example,…
The abstract Cauchy problem for the distributed order fractional evolution equation in the Caputo and in the Riemann-Liouville sense is studied for operators generating a strongly continuous one-parameter semigroup on a Banach space.…
In difference algebra, summability arises as a basic problem upon which rests the effective solution of other more elaborate problems, such as creative telescoping problems and the computation of Galois groups of difference equations. In…
This paper is mainly concerned with the Cauchy problem for a generalized Camassa-Holm equation with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time. Then, we present…
In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental…
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
Working in the p-adic analog of the complex numbers, we'll define a line integral on a small arc of a circle. This allows new versions of the Residue Theorem, the Cauchy-Goursat Theorem on discs with and without holes, Cauchy's Integral…
In this paper, we study the class of one dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.