相关论文: Appell Transformation and Canonical Transforms

A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently [S. Guenneau, C. Amra, and D. Veynante, Optics Express Vol. 20, 8207-8218 (2012)]. A detailed derivation of this…

The lower order terms of the heat kernel expansion at coincident points are computed in the context of finite temperature quantum field theory for flat space-time and in the presence of general gauge and scalar fields which may be non…

We investigate the structure of the Schrodinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which…

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…

In the first part of this paper, we study the heat equation and the heat kernel associated with the Heckman-Opdam Laplacian in the compact, Weyl-group invariant setting. In particular, this Laplacian gives rise to a Feller-Markov semigroup…

We develop a differential theory for the polarity transform parallel to that for the Legendre transform, which is applicable when the functions studied are "geometric convex", namely convex, non-negative and vanish at the origin. This…

We develop a theory of heat transfer induced by thermal charge fluctuations in two-dimensional electron double layers. We consider pristine systems comprised of identical layers, and focus on the regime of sufficiently high temperatures and…

We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…

In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…

A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…

We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…

The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the…

A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…

The two-dimensional (2D) offset linear canonical transform (OLCT) in polar coordinates plays an important role in many fields of optics and signal processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we extend the 2D…

We investigate heat propagation in rigidly rotating bodies within the theory of general relativity. Using a first-order gradient expansion, we derive a universal partial differential equation governing the temperature evolution. This…

It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…

In this paper, we consider the heat equation with the natural polynomial non-linear term; and with two different cases in the diffusion term. The first case (anomalous diffusion) concerns the fractional Laplacian operator with parameter…

This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…

We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…