Accession Number : AD0693525

Title :   CONVERGENCE CONDITIONS AND ESTIMATION OF ERROR IN AN APPROXIMATE INVERSION OF A LAPLACE TRANFORM WITH THE AID OF A FOURIER SERIES,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Krylov,V. I. ; Skoblya,N. S.

Report Date : 30 JUN 1969

Pagination or Media Count : 9

Abstract : It is pointed out that the solution of many problems in mechanics and engineering by means of the Laplace transformation is reduced to the problem of determining the inverse function f(t) from its known Laplace transform F(p). For determining f(t), expanded in Fourier series in sines and in cosines, the values of F(p) in the integer points are used. The problem of the convergence of these series and an estimate of the remainder for certain classes of functions are analyzed. As in the majority of applied problems the properties of f(t) are unknown, and only the Laplace transform F(p) is known, the authors try to formulate the convergence conditions and to determine the remainder in terms of F(P). Two theorems are proved establishing conditions which must be imposed upon F(p) so that the above-mentioned Fourier expansions of f(t) in sines and cosines uniformly converge. The asymptotic expressions are derived for their remainders. (Author)

Descriptors :   (*INTEGRAL TRANSFORMS, APPROXIMATION(MATHEMATICS)), (*FOURIER ANALYSIS, SERIES(MATHEMATICS)), (*SERIES(MATHEMATICS), CONVERGENCE), ANALYTIC FUNCTIONS, ASYMPTOTIC SERIES, ERRORS, THEOREMS, USSR

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE