相关论文: Spectral Reciprocity: A Fourier--Analytic Approach

In this article, we investigate spectral properties of the sublaplacian $-\Delta_{G}$ on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approach to the Fourier analysis on the Engel group in terms…

This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at…

We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…

We consider simultaneously two different reductions of a Zakharov-Shabat's spectral problem in pole gauge. Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of the recursion operators related to the…

A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach…

In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors…

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate…

We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions…

Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(\vartheta,\varphi)$, $|m| \leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre…

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…

We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…

We present linear response theories in the continuum capable of describing continuum spectra and dynamical correlations of finite systems with no spatial symmetry. Our formulation is essentially the same as the continuum random-phase…

We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for solving the homogeneous Boltzmann equation to compute the low probability tails of the velocity distribution function, $f$, of a particle species. This method is based…

In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…

Non-linear interactions during inflation generate non-Gaussianities in the distribution of primordial curvature. In many theories, the physics is scale-invariant, such that the induced three-point function depends solely on a dimensionless…

An extension may be proposed to the intensity interferometer of Hanbury Brown and Twiss to provide the Fourier phase measurement by the use of third-order intensity correlations. It is well known that interferometric reconstruction of…

We evaluate the Gutzwiller trace formula for the level density of classically chaotic systems by considering the level density in a bounded energy range and truncating its Fourier integral. This results in a limiting procedure which…

We investigate and review how Fourier transform is involved in the analysis of a twisted group algebra $L^1(G, \sigma)$ for $G=\widehat{\Gamma}\times \Gamma$ and $\sigma:G\times G \to \mathbb{T}$ 2- cocycle where $\Gamma$ is a locally…

For a fundamental solution of Laplace's equation on the $R$-radius $d$-dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion…

We present an analytical and numerical solution of the calculation of the transition moments for the exact semi-classical light-matter interaction for wavefunctions expanded in a Gaussian basis. By a simple manipulation we show that the…