APPLICATIONS OF THE STATIONARY PHASE FORMULA TO SOLUTIONS OF THE HELMHOLTZ EQUATION IN EXTERIOR DOMAINS.

Title: APPLICATIONS OF THE STATIONARY PHASE FORMULA TO SOLUTIONS OF THE HELMHOLTZ EQUATION IN EXTERIOR DOMAINS.
Identifier: AAI8501168
identifier: 8501168
Creator: RYWKIN, RICHARD J. F.
Contributor: Richard Sacksteder
Date: 1984
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this paper we generalize the stationary phase formula to first provide any desired number of terms in the asymptotic expansion of integrals of the type (INT)(,(SUMM)) e('ik(phi)(y)) a(y)dy for large k and second to extend the stationary phase formula so as to treat integrals like the above which possess singularities in a(y) at isolated points, even in cases where (phi) is not differentiable at the singularity. Some lemmas are also presented which evaluate integrals of the type.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;(derivable from the above) and give order of magnitude estimates for the remainder terms of the asymptotic expansion under certain assumptions on h where the interval (a,b) is either infinite or semi-infinite.;The generalized formula is then applied to two related integral operators which are used to determine solutions of the Helmholtz equation. As an example of the use of the method the case of 2-dimensional surfaces is examined in detail and the classical results are rederived.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics

Media: APPLICATIONS OF THE STATIONARY PHASE FORMULA TO SOLUTIONS OF THE HELMHOLTZ EQUATION IN EXTERIOR DOMAINS.