Related papers: Modified Stieltjes Transform and Generalized Convo…
We study analytic and geometric properties of Stieltjes and inverse Stieltjes families defined on a separable Hilbert space and establish various minimal representations for them by means of compressed resolvents of various types of linear…
A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
Some new integrals involving the Stieltjes constants are developed in this paper.
A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order, and are not necessarily smooth. We show that such functions have a unique integral…
The general framework of Legendre transformation is extended to the case of symplectic groupoids, using an appropriate generalization of the notion of generating function (of a Lagrangian submanifold).
Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented…
The practical usefulness of Levin-type nonlinear sequence transformations as numerical tools for the summation of divergent series or for the convergence acceleration of slowly converging series, is nowadays beyond dispute. Weniger's…
The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. The dichotomy is modulated by allowing more than one negative eigenvalue…
We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated
This paper deals with the delta continuous Stieltjes variational integral generalized in the plane. In particular, this work presents about some fundamental properties of it. The delta continuous Stieltjes variational integral in the plane…
Miller-Paris transformations are extensions of Euler's transformations for the Gauss hypergeometric functions to generalized hypergeometric functions of higher-order having integral parameter differences (IPD). In our recent work we…
In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally…
Some new integrals involving the Stieltjes constants are developed in this paper.
In this note, we recall Kummer's Fourier series expansion of the 1-periodic function that coincides with the logarithm of the Gamma function on the unit interval $(0,1)$, and we use it to find closed forms for some numerical series related…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds…
Generalized Lorentz transformations with modified velocity parameter are considered. Lorentz transformations depending on the mass of the observer are suggested.The modified formula for the addition of velocities remarkably preserves the…
In this work, we extend the concept of the Stieltjes derivative to encompass left-continuous derivators with bounded variation, thereby relaxing the monotonicity constraint. This generalization necessitates a refined definition of the…
We present a new representation of the Stieltjes constants in the form of a limit of a Fourier series.