This memoir presents a simple sequential definition of the Feynman integral -which
is applicable to a rather large class of functionals. The existence theorem shows that
this sequential Feynman integral exists and equals the analytic Feynman for all elements
of a Banach algebra of functionals expressable as Fourier transforms of measures of
finite variation on Lp . This integral has good translation and rotation properties
and permutes with other integrals and sums in a reasonable way. Applications to the
Schroedinger equation are given and the relationship to other sequential definitions
1980 Mathematics Subject Classification 28C20
KEY WORDS AND PHRASES
Sequential Feynman Integral,Analytic Feynman Integral,Feynman Path Integral,
Integration in Function Space,Fourier Transforms in Function Space,Schroedinger Equation.
Library of Congress Cataloging in Publication Data
Cameron, Robert Horton, 1908-
A simple definition of the Feynman integral, vith
(Memoirs of the American Mathematical Society,
ISSN 0065-9266 ; no. 288)
1. Feynman integral. 2. Function spaces.
I. Storvick, David Arne, 1929- . II. Series.
QA3.A57 no. 288 510s £515.^'23 83-15605