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We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.
We develop some properties and the Bonnet formula for Clifford Gegenbauer polynomials. Then after we define and construct weighted Clifford prolate spheroidal wave functions. We then prove that they are orthogonal in a weighted function…
For the minimal graph with strict convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.
We describe a general correspondence between weighted minimal surfaces in $\mathbb{R}^3$ and weighted maximal surfaces with some admissible singularities in $\mathbb{L}^3$, for a class of functions $\varphi$ which provides the corresponding…
In this paper, we study the problem of finding the affine factorable surfaces in a 3-dimensional isotropic space with prescribed Gaussian (K) and mean (H) curvature. Because the absolute figure two different types of these surfaces appear…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
We describe a new approach to the notion of general hypergeometric functions
The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have…
In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…
In this paper, based on concepts of convex sets and convex functions, we introduce new concepts of functions, Young functions, strong Young functions and Orlicz functions by relaxing definitions of functions, Young functions, strong Young…
We want to investigate 'spaces' where paths have a 'weight', or 'cost', expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to path-reversion. Thus, 'weighted algebraic topology' can be…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…