Related papers: The Mehler-Fock Transform and some Applications in…
In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including…
We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge…
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…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincar\'e theory. In the metamorphosis of images, the Lie group of diffeomorphisms deforms…
In the quest to realize analog signal processing using sub-wavelength metasurfaces, in this paper, we demonstrate the first experimental demonstration of programmable time-modulated metasurface processors based on the key properties of…
The spherical Fourier transform on a harmonic Hadamard manifold $(X^n, g)$ of positive volume entropy is studied. If $(X^n, g)$ is of hypergeometric type, namely spherical functions of $X$ are represented by the Gauss hypergeometric…
Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a…
The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
Liu and Liu introduced the random Fourier transform, which is a random Fourier series in Hermite functions, and applied it to image encryption and decryption. They expected its applications in optics and information technology. These…
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…
We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and…
These are notes of a talk based on the work arXiv:1212.3630 joint with A. Aizenbud. Let V be a finite-dimensional vector space over a local field F of characteristic 0. Let f be a function on V of the form $f(x)= \psi (P(x))$, where P is a…
This paper outlines a method where a brachistochrone is developed for the hyperbolic plane. This technique is then used to calculate the Fubini-Study metric and consequent Laplacian operator. We discuss the various systems of eigenfunctions…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer…