Ebook: Functional Analysis: Vol. I

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical 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 advanced 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.

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"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical 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 advanced 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.

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"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical 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 advanced 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.
Content:
Front Matter....Pages i-xix
Measure Theory....Pages 1-65
Measurable Functions....Pages 67-88
Theory of Integration....Pages 89-132
Measures in the Products of Spaces. Fubini Theorem....Pages 133-145
Absolute Continuity and Singularity of Measures, Charges, and Functions. Radon-Nikodym Theorem. Change of Variables in the Lebesgue Integral....Pages 147-176
Linear Normed Spaces and Hilbert Spaces....Pages 177-214
Linear Continuous Functionals and Dual Spaces....Pages 215-271
Linear Continuous Operators....Pages 273-320
Compact Operators. Equations with Compact Operators....Pages 321-354
Spectral Decomposition of Compact Selfadjoint Operators. Analytic Functions of Operators....Pages 355-384
Elements of the Theory of Generalized Functions....Pages 385-410
Back Matter....Pages 411-423

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"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical 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 advanced 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.
Content:
Front Matter....Pages i-xix
Measure Theory....Pages 1-65
Measurable Functions....Pages 67-88
Theory of Integration....Pages 89-132
Measures in the Products of Spaces. Fubini Theorem....Pages 133-145
Absolute Continuity and Singularity of Measures, Charges, and Functions. Radon-Nikodym Theorem. Change of Variables in the Lebesgue Integral....Pages 147-176
Linear Normed Spaces and Hilbert Spaces....Pages 177-214
Linear Continuous Functionals and Dual Spaces....Pages 215-271
Linear Continuous Operators....Pages 273-320
Compact Operators. Equations with Compact Operators....Pages 321-354
Spectral Decomposition of Compact Selfadjoint Operators. Analytic Functions of Operators....Pages 355-384
Elements of the Theory of Generalized Functions....Pages 385-410
Back Matter....Pages 411-423
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