Related papers: $q$-Bessel Fourier Transform and Variation Diminis…
We use the Poisson kernel of the continuous $q$-Hermite polynomials to introduces families of integral operators, which are semigroups of linear operators. We describe the eigenvalues and eigenfunctions of one family of operators. The…
In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of…
We present a method for the numerical computation of Fourier-Bessel transforms on a finite or infinite interval. The function to be transformed needs to be evaluated on a grid of points that is independent of the argument of the Bessel…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We study special values for the continuous $q$-Jacobi polynomials and present applications of these special values which arise from bilinear generating functions, and in particular the Poisson kernel for these polynomials.
We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators…
This is a study of $q$-Fermions arising from a q-deformed algebra of harmonic oscillators. Two distinct algebras will be investigated. Employing the first algebra, the Fock states are constructed for the generalized Fermions obeying Pauli…
We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
In this paper, we define the notions $q$-birational morphism and $q$-birational divisor and develop the theory about them. We state and prove versions of Kodaira-type vanishing theorem and Zariski decomposition theorem for $q$-birational…
An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel $|K_{(i\tau+\alpha)/2}(x)|^2, \alpha \ge 0,\ x…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
This paper aims to study the $q$-wavelet and the $q$-wavelet transforms, associated with the $q$-Bessel operator for a fixed $q\in ]0, 1[$. As an application, an inversion formulas of the $q$-Riemann-Liouville and $q$-Weyl transforms using…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…
The concept of $q$-deformation, or ``$q$-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; $q$-deformations are important for knot invariants, combinatorial…
In this paper, we pursue the investigations started in \cite{Mas-You} where the authors provide a construction of the Dunkl intertwining operator for a large subset of the set of regular multiplicity values. More precisely, we make concrete…
We consider the existence of convolution of Roumieu type ultradistribution with the kernel $e^{s(1+|x|^2)^{q/2}}, q\geq 1$, $s\in\RR\backslash\{0\}$.
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…