Related papers: Modified Stieltjes Transform and Generalized Convo…
We enlarge the hom-sets of categories of complete lattices by introducing `state transitions' as generalized morphisms. The obtained category will then be compared with a functorial quantaloidal enrichment and a contextual quantaloidal…
The functions studied in the paper are quaternion-valued functions of a quaternionic variable. It is show that the left slice regular functions and right slice regular functions are related by a particular involution. The relation between…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…
A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
Classical {\W}$_3$ transformations are discussed as restricted diffeomorphism transformations (\W-Diff) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended {\W}$_3$ generators are…
Using Pathak and Pathak techniques, the basic function $D^\alpha(u,v,w)$ associated with general novel fractional wavelet transform (GNFrWT)is defined and its properties are investigated. By using basic function $D^\alpha(u,v,w)$…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
A small set of combinatorial sequences have coefficients that can be represented as moments of a nonnegative measure on $[0, \infty)$. Such sequences are known as Stieltjes moment sequences. This article focuses on some classical sequences…
The goal of this article is to generalise the Witten deformation to even dimensional conic manifolds and a class of functions called admissible Morse functions.
In this paper holomorphic families of linear relations which belong to the Stieltjes or inverse Stieltjes class are studied. It is shown that in their domain of holomorphy ${\mathbb C}\setminus{\mathbb R}_+$ the values of Stieltjes and…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator. The proposed technique, along with the use of the relevant operational…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…