We give an explicit formula (i.e., a formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. Résumé (Une formule de la phase stationnaire explicite pour le transformé de Fourier-Laplace local) On donne une formule explicite (c’est-à-dire une formule de la phase stationnaire...

Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the Hankel transform with respect to the radial coordinate r, the finite Fourier transform with respect to the angular coordinate φ, and the exponential Fourier transfor...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

In this paper we describe two numerical methods by which the relaxation modulus and memory function of a polymer can be determined from a set of discrete linear viscoelastic storage and loss moduli measurements. The first method involves expressing the linear viscoelastic data by means of a rational function (with certain constraints) and then taking the Laplace transform of that function. The ...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

Harmonic analysis studies the representation of functions as the linear combination of basic wave-like functions. It plays a fundamental role in the processing of time-series signals and images. Recent years have witnessed many efforts to adapt the Fourier and wavelet analysis to the domain of 3D shapes. The manifold Fourier analysis relies on the eigenfunctions of the Laplace-Beltrami operator...

We give an explicit formula (i.e., an explicit expression for the formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. Introduction We will denote by C((t)) (resp. C({t})) the field C[[t]][t] (resp. C{t}[t]) of formal (resp. convergent) Laurent series of the variable t, ...