文档介绍：TRANSMUTATION AND
OPERATOR DIFFERENTIAL EQUATIONS
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NORTH-HOLLAND
MATHEMATICS STUDIES 37
Notas de Matematica (67)
Editor: Leopoldo Nachbin
Universidade Federal do Rio de Janeiro
and University of Rochester
Transmutation.
and
Operator Differential Equations
R. W. Carroll
Mathematics Department
University of Illinois
1979
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Lihrary of Congress Calaloging in Publication Data
Carroll, Robert Wayne, 1930-
Transmutation and operator differential
equations.
(Notas de matem&icas ; 67) (North-Holland
mathematics studies j 37)
1. Differential equations, Partial.
2. Operator equations. I. Title. 11. Series.
no. 67 [QAj74] ~[515'.353] 79-12341
ISBN 0-444 -85328 -6
PRINTED IN HERLANDS
PREFACE
With the advent of modern functional analysis and the theory of distributions it
became possible in the early 1950's to systematically explore and develop the
theory of partial differential equations (PDE) to a degree previously unimaginable.
One important feature of this work was the determination of "natural" spaces of
functions of distributions in which to pose various differential problems. Then
linear differential operators were treated as abstract linear operators A mapping
a domain of definition D(A) C F into G for suitable locally convex topological
vector spaces F and G. The abstract operational properties of A we