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Softcover ISBN:  9780821815892 
Product Code:  MMONO/39 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470444549 
Product Code:  MMONO/39.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821815892 
eBook ISBN:  9781470444549 
Product Code:  MMONO/39.B 
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MAA Member Price:  $288.00 $218.25 
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Book DetailsTranslations of Mathematical MonographsVolume: 39; 1975; 525 ppMSC: Primary 34; Secondary 47
This monograph is devoted to the spectral theory of the Sturm Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.

Table of Contents

Chapters

Expansion in a Finite Interval

Eigenfunction Expansions for a SturmLiouville Operator for the Case of an Infinite Interval

Expansion in the Singular Case for a Dirac System

Investigation of the Spectrum

Examples

Solution of the Cauchy Problem for the Onedimensional Wave Equation

Eigenfunction Expansion of a SturmLiouville Operator

Differentiation of an Eigenfunction Expansion

Solution of the Cauchy Problem for a OneDimensional Dirac System

Asymptotic Behaviour of the Spectral Kernel and its Derivatives for the Case of a Dirac System

Expansion, and Differentiation of an Expansion, with Respect to the Eigenfunctions of a Dirac System

Asymptotic Behaviour of the Number of Eigenvalues of a SturmLiouville Operator

Elements of the Spectral Theory of Linear Operators in Hilbert Space. Relation to Differential Operators

Some Theorems of Analysis


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This monograph is devoted to the spectral theory of the Sturm Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.

Chapters

Expansion in a Finite Interval

Eigenfunction Expansions for a SturmLiouville Operator for the Case of an Infinite Interval

Expansion in the Singular Case for a Dirac System

Investigation of the Spectrum

Examples

Solution of the Cauchy Problem for the Onedimensional Wave Equation

Eigenfunction Expansion of a SturmLiouville Operator

Differentiation of an Eigenfunction Expansion

Solution of the Cauchy Problem for a OneDimensional Dirac System

Asymptotic Behaviour of the Spectral Kernel and its Derivatives for the Case of a Dirac System

Expansion, and Differentiation of an Expansion, with Respect to the Eigenfunctions of a Dirac System

Asymptotic Behaviour of the Number of Eigenvalues of a SturmLiouville Operator

Elements of the Spectral Theory of Linear Operators in Hilbert Space. Relation to Differential Operators

Some Theorems of Analysis