Spectral Theory of Ordinary Differential Operators
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differentia
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1258 Joachim Weidmann
Spectral Theory of Ordinary Differential Operators
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann
1258 Joachim Weidmann
Spectral Theory of Ordinary Differential Operators
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Author
Joachim Weidmann Fachbereich Mathematik, Universitat Frankfurt Robert-Mayer-Stral3e 6-10, Postfach 111932 6000 Frankfurt/Main 11, Federal Republic of Germany
Mathematics Subject Classification (1980): 35B25, 35PXX, 47A40, 47E05, 81 C 10 ISBN 3-540-17902-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387 -17902-X Springer-Verlag New York Berlin Heidelberg
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Preface
Hermann Weyl's celebrated work from 1910
"Uber gewohnl.Lche Differen-
tialgleichungen mit Singularitaten und die zugehorigen Entwicklungen willktirlicher Funktionen"
together with the developement of quantum mechanics
around 1925 initiated a continuous and extremely fruitful research activity in the spectral theory of Sturm-Liouville operators. Although the general theory in some sense had reached its final shape with the proof of the spectral
representation and the WeylTitchmarsh formula for the
spectral
matrix, many fascinating results about special operators have been contributed by a large number of mathematicians up to the present days. Wide
parts of the theory were generalized long time ago
even order operators mainly by On
the
other
Titchmarsh Liouville no
results case
expressions was
hand
by
have
B.W. Roos,
W.C. Sangren
are almost identical to those
been found for
operating on
[;2
certain
I.M. Glazman, K. Kodaira and M.A. Neumark.
S.D. Conte,
which
to
certain
first
in
order
the
E.C.
Sturm-
differential
valued functions (Dirac systems).
general frame including all these different
and
types,
But
there
although
it
seemed obvious that there were many common features. The starting point for writing these notes was the intention to sent a general theory of ordinary differential operators, tors
of
trary the
m.
arbitrary order
covering opera-
operating on [;valued functions
for
arbi-
This is the content of about two thirds of the present text. In
remaining part we apply this theory to SturmLiouville operators
Dirac systems, of
n
pre-
studying mai
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