In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this p...

In this article we prove that if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff–type condition, then the series converges to a function which admits a holomorphic extension to a cut–plane. Furthermore, we prove that a Laplace–type (Laplace composed with Radon) transform of the function describing the jump across the cut is the unique Carlsonian interpolation of th...

This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of (FT). The Unilateral Laplace (LT) observed to be special case GFT. GFT, as proposed in this work, contributes significantly scholarly literature. There are many salient contribution work. Firstly, GFT applicable a much larger class signals, some which cannot analyzed with FT and LT. For examp...

Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is ge...

A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the...

Abstract. A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function...

In this paper, we develop a simple three layered neural network for recognition the invariant contour of image. Our approach relies on a method which normalizes the Fourier Descriptors (FDs) of image contour with its Laplace transform. Our approach is inspired the observations that the traditional Fourier transform of a 1-D is equivalent to the 2-D of image recognition. We compare between them ...