f(x) det(xx)dx and the Radon transform on the space Mn,m of n × m real matrices x = (xi,j). We present a self-contained proof of the Fourier transform formula for this distribution. Our method differs from that of J. Faraut and A. Korányi [FK] in the part related to justification of the corresponding Bernstein identity. We suggest a new proof of this identity based on explicit representation of...

This work is devoted to the nondestructive evaluation of materials using stimulated infrared thermography. The proposed approach provides simple analytical solutions to evaluate the lateral extent, and the thickness of a plane flaw in a three-dimensional (3D) heat transfer configuration. It is based on the application of a Laplace transform on the time variable t, then a double Fourier transfor...

Let G be the split solvable Lie group acting simply transitively on a Siegel domain D. We consider irreducible unitary representations of G realized on Hilbert spaces of holomorphic functions on D. We determine all such Hilbert spaces by connecting them with positive Riesz distributions on the dual cone and describe them through the Fourier-Laplace transform. Moreover we classify the representa...

— We show that the limit, by rescaling, of the ‘new supersymmetric index’ attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of comple...

To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems. Traditionally, Fourier transform methods are used to perform this frequency domain analysis using paper-and-pencil based analytical techniques or computer simulati...

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis is based on bounds derived by relative entropy inequalities and on two recently developed approaches for the macroscopic limit: a Fourier-Lap...

The present investigation deals with the deformation in micropolar generalized thermoelastic medium with mass diffusion subjected to thermo mechanical loading due to thermal laser pulse. Laplace and Fourier transform technique is used to solve the problem. Concentrated normal force and thermal source are taken to illustrate the utility of approach. The closed form expressions of normal stress, ...

We consider the Laplace equation under mixed boundary conditions on a polygonal domain Ω. Regularity estimates in terms of Sobolev norms of fractional order for this type of problem are proved. The analysis is based on new interpolation results and multilevel representation of norms on the Sobolev spaces Hα(Ω). The Fourier transform and the construction of extension operators to Sobolev spaces ...

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then, by using the Mellin transform, a general representation of the Green function in terms of Mellin-Barnes integrals in the complex plane is derived. This allow...

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light...