WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
The Fourier Transform with Piecewise Trigonometric Kernels and its Applications
Authors: , ,
Abstract: In this paper, we develop a theory of the Fourier integral transforms with piecewise-homogeneous trigonometric kernels. Formulas for Integral transforms are obtained in a Hermite-type orthogonal polynomials series form. The resulting formulas are new for both the classical and piecewise- homogeneous cases. In the sec- ond part of the article method of Hermite-type orthogonal polynomials series expansion is used to solve the direct and inverse Cauchy problems for the heat equation in a piecewise- homogeneous medium. The inverse Cauchy problem is ill-posed and requires regularization. Formulas for solving direct and inverse Cauchy problems are obtained by the developed method and have advantages: first, they do not contain derivatives, can serve as a basis for regularizing algorithms , and secondly, these formulas are mutually symmetrical.
Search Articles
Pages: 615-625
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #60