Related papers: $q$-Bessel Fourier Transform and Variation Diminis…
The content of this work is concerned with Jordan-Schwinger calculus using $q$-deformed bosons.
The Fueter-Sce-Qian (FSQ for short) mapping theorem is a two-steps procedure to extend holomorphic functions of one complex variable to slice monogenic functions and to monogenic functions. Using the Cauchy formula of slice monogenic…
This paper deals with the study of the zeros of the big $q$-Bessel functions. In particular, we prove a new orthogonality relations for this functions similar to the one for the classical Bessel functions. Also we give some applications…
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
For functions that take values in the Clifford algebra, we study the Clifford-Fourier transform on $R^m$ defined with a kernel function $K(x,y) := e^{\frac{i \pi}{2} \Gamma_{y}}e^{-i <x,y>}$, replacing the kernel $e^{i <x,y>}$ of the…
In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse…
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…
In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of…
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
We develop a general method for lower bounding the variance of sequences in arithmetic progressions mod $q$, summed over all $q \leq Q$, building on previous work of Liu, Perelli, Hooley, and others. The proofs lower bound the variance by…
By considering semi-inclusive deep-inelastic scattering and the (complementary) $q_T$-spectrum for Drell-Yan lepton pair production we derive the QCD evolution for all the leading-twist transverse momentum dependent distribution and…
We introduce a $q$-deformation that generalises in a single framework previous works on classical and enriched $P$-partitions. In particular, we build a new family of power series with a parameter $q$ that interpolates between Gessel's…
In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and…
We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship…
We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…
In this paper, we study $q$-difference analogues of several central results in value distribution theory of several complex variables such as $q$-difference versions of the logarithmic derivative lemma, the second main theorem for…
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and…
In this paper, we show that the kernel function of Cauchy type for type $BC$ intertwines the commuting family of van Diejen's $q$-difference operators. This result gives rise to a transformation formula for certain multiple basic…