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We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
We prove an extension of the Stein-Weiss weighted estimates for fractional integrals, in the context of Lp spaces with different integrability properties in the radial and the angular direction. In this way, the classical estimates can be…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…
After an elementary derivation of Bell's inequality, several forms of expectation functions for two-valued observables are discussed. Special emphasis is given to hypothetical stronger-than quantum expectation functions which give rise to a…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…
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,…
Some Tur\'an type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind. New formulas, like Mittag-Leffler expansion, infinite product…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…