Related papers: On certain functions and related problems
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…
We introduced a new algebra of stochastic generalized functions which contains to the space of stochastic distributions G, [25]. As an application, we prove existence and uniqueness of the solution of a stochastic Cauchy problem involving…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using…
We consider solvable matrix models. 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…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and…
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…
The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
This is a survey of the author's recent results on the Kadison and Halmos similarity problems and the closely connected notion of ``length'' of an operator algebra.