Hardcover ISBN:  9780821820490 
Product Code:  SURV/73 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413002 
Product Code:  SURV/73.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821820490 
eBook: ISBN:  9781470413002 
Product Code:  SURV/73.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821820490 
Product Code:  SURV/73 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413002 
Product Code:  SURV/73.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821820490 
eBook ISBN:  9781470413002 
Product Code:  SURV/73.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 73; 2000; 252 ppMSC: Primary 34; 47
This monograph develops the spectral theory of an \(n\)th order nonselfadjoint twopoint differential operator \(L\) in the Hilbert space \(L^2[0,1]\). The mathematical foundation is laid in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. An important completeness theorem is established for the HilbertSchmidt discrete operators. The operational calculus plays a major role in this general theory.
In the second part, the spectral theory of the differential operator \(L\) is developed by expressing \(L\) in the form \(L = T + S\), where \(T\) is the principal part determined by the \(n\)th order derivative and \(S\) is the part determined by the lowerorder derivatives. The spectral theory of \(T\) is developed first using operator theory, and then the spectral theory of \(L\) is developed by treating \(L\) as a perturbation of \(T\). Regular and irregular boundary values are allowed for \(T\), and regular boundary values are considered for \(L\). Special features of the spectral theory for \(L\) and \(T\) include the following: calculation of the eigenvalues, algebraic multiplicities and ascents; calculation of the associated family of projections which project onto the generalized eigenspaces; completeness of the generalized eigenfunctions; uniform bounds on the family of all finite sums of the associated projections; and expansions of functions in series of generalized eigenfunctions of \(L\) and \(T\).
ReadershipGraduate students and research mathematicians interested in ordinary differential equations.

Table of Contents

Chapters

1. Unbounded linear operators

2. Fredholm operators

3. Introduction to the spectral theory of differential operators

4. Principal part of a differential operator

5. Projections and generalized eigenfunction expansions

6. Spectral theory for general differential operators


Additional Material

Reviews

An uptodate account of the spectral theory of nonselfadjoint ordinary differential equations on a compact interval of the real line ... This book is well written and is accessible to all who have a rudimentary knowledge of functional analysis. It is well suited both to graduate students working in twopoint boundary value problems and to other scientists seeking further information concerning them.
Bulletin of the LMS 
Detailed proofs are given; this, together with the introductory material of the first two chapters, should make the book accessible to a good graduate student with some background in functional analysis and differential equations. The monograph will probably appeal mainly to specialists.
Mathematical Reviews


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This monograph develops the spectral theory of an \(n\)th order nonselfadjoint twopoint differential operator \(L\) in the Hilbert space \(L^2[0,1]\). The mathematical foundation is laid in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. An important completeness theorem is established for the HilbertSchmidt discrete operators. The operational calculus plays a major role in this general theory.
In the second part, the spectral theory of the differential operator \(L\) is developed by expressing \(L\) in the form \(L = T + S\), where \(T\) is the principal part determined by the \(n\)th order derivative and \(S\) is the part determined by the lowerorder derivatives. The spectral theory of \(T\) is developed first using operator theory, and then the spectral theory of \(L\) is developed by treating \(L\) as a perturbation of \(T\). Regular and irregular boundary values are allowed for \(T\), and regular boundary values are considered for \(L\). Special features of the spectral theory for \(L\) and \(T\) include the following: calculation of the eigenvalues, algebraic multiplicities and ascents; calculation of the associated family of projections which project onto the generalized eigenspaces; completeness of the generalized eigenfunctions; uniform bounds on the family of all finite sums of the associated projections; and expansions of functions in series of generalized eigenfunctions of \(L\) and \(T\).
Graduate students and research mathematicians interested in ordinary differential equations.

Chapters

1. Unbounded linear operators

2. Fredholm operators

3. Introduction to the spectral theory of differential operators

4. Principal part of a differential operator

5. Projections and generalized eigenfunction expansions

6. Spectral theory for general differential operators

An uptodate account of the spectral theory of nonselfadjoint ordinary differential equations on a compact interval of the real line ... This book is well written and is accessible to all who have a rudimentary knowledge of functional analysis. It is well suited both to graduate students working in twopoint boundary value problems and to other scientists seeking further information concerning them.
Bulletin of the LMS 
Detailed proofs are given; this, together with the introductory material of the first two chapters, should make the book accessible to a good graduate student with some background in functional analysis and differential equations. The monograph will probably appeal mainly to specialists.
Mathematical Reviews