Functional Analysis Vol.II [Paperback]

Functional Analysis is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathemati- cal physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more ad- vanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.Functional Analysis is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathemati- cal physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more ad- vanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.12 General Theory of Unbounded Operators in Hilbert Spaces.- 1 Definition of an Unbounded Operator. The Graph of an Operator.- 1.1 Definitions.- 1.2 Graphs of Operators.- 2 Closed and Closable Operators. Differential Operators.- 2.1 Closed Operators.- 2.2 Closable Operators.- 2.3 Differential Operators.- 3 The Adjoint Operator.- 3.1 Definition and Properties of the Adjoint Operator.- 3.2 The Second Adjoint Operator.- 3.3 The Closed Graph Theorem.- 4 Defect Numbers of General Operators.- 4.1 Deficient Subspaces.- 4.2 Defect Numbers.- 5 Hermitian and Selfadjoint Operators. General Theory.- 5.1 Hermitian Operators.- 5.2 CrilÃ)