Related papers: k-Deformed Fourier Transform
In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the $(\kappa, a)$-generalized Fourier transform for $\kappa =0$. In the case of dihedral groups, this method is also applied to the Dunkl…
In this paper, we study the pointwise bounds for the kernel of the $(\kappa, a)$-generalized Fourier transform with $\kappa\equiv0$, introduced by Ben Sa\"id, Kobayashi and Orsted. We present explicit formulas for the case $a=4$, which show…
We present the main features of the mathematical theory generated by the \kappa-deformed exponential function exp_{\kappa}(x)=(\sqrt{1+\kappa^2 x^2}+\kappa x)^{1/\kappa}, with 0<\kappa<1, developed in the last twelve years, which turns out…
Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter deformation for the exponential function $\exp_{_{\{{\scriptstyle \kappa}\}}}(x)= (\sqrt{1+\kappa^2x^2}+\kappa x)^{1/\kappa}; \exp_{_{\{{\scriptstyle 0}\}}}(x)=\exp…
A recent generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted $q$-Fourier transform. A representation formula for the…
We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa}…
We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered,…
The radially deformed Fourier transform, introduced in [S. Ben Said, T. Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio Math.], is an integral transform that depends on a numerical parameter $a \in R^{+}$. So…
We deform Heisenberg algebra and corresponding coalgebra by twist. We present undeformed and deformed tensor identities. Coalgebras for the generalized Poincar\'{e} algebras have been constructed. The exact universal $R$-matrix for the…
We propose new noncommutative models of quantum phase spaces, containing a pair of $\kappa$-deformed Poincar\'e algebras, with two independent double ($\kappa,\tilde{\kappa}$)-deformations in space-time and four-momenta sectors. The first…
A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…
The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
We provide first explicite examples of quantum deformations of D=4 conformal algebra with mass-like deformation parameters, in applications to quantum gravity effects related with Planck mass. It is shown that one of the classical…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
For the kernel $B_{\kappa,a}(x,y)$ of the $(\kappa,a)$-generalized Fourier transform $\mathcal{F}_{\kappa,a}$, acting in $L^{2}(\mathbb{R}^{d})$ with the weight $|x|^{a-2}v_{\kappa}(x)$, where $v_{\kappa}$ is the Dunkl weight, we study the…
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 the following work we will introduce and discuss in detail a particular model of complex $\kappa$-deformed scalar field, whose behaviour under C, P , T transformation is particularly transparent from both a formal and phenomenological…
We extend our previous study of Hopf-algebraic $\kappa$-deformations of all inhomogeneous orthogonal Lie algebras ${\rm iso}(g)$ as written in a tensorial and unified form. Such deformations are determined by a vector $\tau$ which for…
In a related paper we have obtained that the effective action for a kappa-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the kappa-deformed zero mode frequencies, while the imaginary part is…