Related papers: Generalized Functionals in Gaussian Spaces - The C…
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
A new generalized function space in which all Gelfand-Shilov classes $S^{\prime 0}_\alpha$ ($\alpha>1$) of analytic functionals are embedded is introduced. This space of {\it ultrafunctionals} does not possess a natural nontrivial topology…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions.
This article gives an brief outline of the applications of generalized special functions such as generalized hypergeometric functions, G-functions and H-functions into the general area of nuclear energy generation and reaction rate theory…
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…
Building on previous work, we explore the parameter space of general free functions in non-relativistic modified gravity theories motivated by k-essence and other scalar-tensor theories. Using a few proposed tests, we aim to update Solar…
We show that the generalised composition of generalised integral operators is well defined on the space Colombeau algebras of tempered generalised functions.
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
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.
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…
We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their orbital integrals and transfer to the compact unitary group.…