Related papers: Plancherel theorem and quaternion Fourier transfor…
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 subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
We extend our previous work (on $D=2$) to give an exact solution of the $\Phi^3_D$ large-$\mathcal{N}$ matrix model (or renormalised Kontsevich model) in $D=4$ and $D=6$ dimensions. Induction proofs and the difficult combinatorics are…
By the important applications of Gabor transform in time-frequency analysis and signal analysis, in this paper, we consider the Gabor quaternion Fourier transform (GQFT), and we prove of it a version Benedicks-type uncertainty principle for…
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 investigate the quaternionic extension of the fractional Fourier transform on the real half-line leading to fractional Hankel transform. This will be handled \`a la Bargmann by means of hyperholomorphic second Bargmann transform for the…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…
Recent advances have extended the Dunkl transform to the setting of Clifford algebras. In particular, the two-sided quaternionic Dunkl transform has been introduced as a Dunkl analogue of the two-dimensional quaternionic Fourier transform.…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
A quadrature mirror filter (QMF) function can be considered as the transition function for a Markov process on the unit interval. The QMF functions that generate scaling functions for multiresolution analyses are then distinguished by…
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…
Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…
We review some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral…
The paper improves the accuracy of the one-dimensional fractional Fourier transform (FRFT) by leveraging closed Newton-Cotes quadrature rules. Using the weights derived from the Composite Newton-Cotes rules of order QN, we demonstrate that…