The Deficiency Index Problem for Powers of Ordinary Differential Expressions
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621 Robert M. Kauffman Thomas 1: Read Anton Zettl
The Deficiency Index Problem for Powers of Ordinary Differential Expressions
Springer-Verlag Berlin Heidelberg New York 1977
Authors Robert M. Kauffman Thomas T.Read Department of Mathematics and Computer Science Western Washington University Bellingham, WA 98225/USA Anton Zettl Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60115/USA
AMS Subject Classifications (1970): 34 B 20, 47 E05 ISBN 3-540-08523-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08523-8 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2140/3140-543210
Preface
These Notes were started when all three authors were visiting the of Dundee in the Spring of 1975.
We are grateful to the University of Dundee and
in particular to Professor W.N.Everitt for the opportunity of this visit and for his suggestion that we undertake this project.
In addition the last named author would
like to thank the British Science Research Council for their financial support. we would like to thank Ms. Barbara Bruns and Ms. Sara Clayton for their careful typing of a difficult manuscript.
R. M. Kauffman and T. T. Read
Anton Zettl Department of Mathematical Sciences Northern Illinois University DeKalb, Illinois
60115
U.S.A.
Department of Mathematics and Computer Science Western Washington University Bellingham, Washington, U.S.A.
Also
Contents Introduction· ..••..••.•••...•... , .•...•. , ....•........• , .. , . .•. . • . .. ... . . .. .. .
1
Chapter 1. Functional Analytic Preliminaries ..•...............................
3
1.
General Operator Theory .•.•.••...••••..•....................•........
3
2.
Symmetric Operators ..••.•....................•.•.....................
4
Chapter II.
Linear Differential Qperators and the General Classification Theory
of Deficiency Indices.
...•••.•.•..........••.••.................•.....••
6
1.
Symmetric Differential Expressions
.••..•..............•.......
6
2.
Deficiency Indices ...........•.•.••.••.•.•••.........................
7
3.
Differential Operators .....•••..........•.......•...................•
10
4.
General Deficiency Indices ...•••••.••..••..•..•.•..................••
16
5.
The General Limit Point Condition
18
6.
Notes and Comments···.····.·.········ ..• ·•·•·••················•··•··
20
Chapter III.
Second Order Limit-Point, Limit-Circle Conditions •...........•.•
22
1.
The General Second Order Theory
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