Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert Space

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John Wiley & Sons, Feb 23, 1988 - Mathematics - 1088 pages
This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.
 

Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space
858
BAlgebras
859
Commutative BAlgebras
868
Commutative BAlgebras
874
Exercises
879
Notes and Remarks
883
Bounded Normal Operators in Hilbert Space
887
The Spectral Theorem for Bounded Normal Operators
895
Notes and Remarks
1145
The Spectral Theorem for Unbounded Self Adjoint Operators
1191
Spectral Representation of Unbounded Self Adjoint Trans
1205
The Extensions of a Symmetric Transformation
1222
Semibounded Symmetric Operators
1241
The Canonical Factorization
1249
Exercises
1259
Notes and Remarks
1271

Eigenvalues and Eigenvectors
902
Unitary Self Adjoint and Positive Operators
905
Spectral Representation
909
A Formula for the Spectral Resolution
920
Perturbation Theory
921
Exercises
923
Notes and Remarks
926
Miscellaneous Applications
937
Almost Periodic Functions
945
Convolution Algebras
949
Closure Theorems
978
Exercises
1001
HilbertSchmidt Operators
1009
The Hilbert Transform and the CalderónZygmund Inequality
1044
Exercises
1073
The Classes C of Compact Operators Generalized Carleman Inequalities
1088
Subdiagonalization of Compact Operators
1119
Ordinary Differential Operators
1278
Adjoints and Boundary Values of Differential Operators
1285
Resolvents of Differential Operators
1311
Compact Resolvents
1331
Qualitative Theory of the Deficiency Index
1393
Qualitative Theory of the Spectrum
1443
Examples
1505
Exercises
1539
Notes and Remarks
1582
Algebras of Spectral Operators
1612
Linear Partial Differential Equations and Operators
1629
The Theorem of Sobolev
1683
Some Geometric Considerations
1701
The Elliptic Boundary Value Problem
1707
APPENDIX
1773
Unbounded Spectral Operators
1789
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About the author (1988)

Nelson James Dunford was an American mathematician, known for his work in functional analysis, namely integration of vector valued functions, ergodic theory, and linear operators. The Dunford decomposition, Dunford-Pettis property, and Dunford-Schwartz theorem bear his name.

Jacob Theodore "Jack" Schwartz was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences. He was the designer of the SETL programming language and started the NYU Ultracomputer project.

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