Functional Analysis Vol. I [Paperback]

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. 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.1 Measure Theory.- 1 Operations on Sets. Ordered Sets.- 1.1 Operations on Sets n2.- 1.2 Ordered Sets. The Zorn Lemma.- 2 Systems of Sets.- 2.1 Rings and Algebras of Sets.- 2.2 ?-Rings and ?-Algebras.- 2.3 Generated Rings and Algebras.- 3 Measure of a Set. Simple Properties of Measures.- 4 Outer Measure.- 5 Measurable Sets. Extension of a Measure.- 6 Properties of Measures and Measurable Sets.- 7 Monotone Classes of Sets. Uniqueness of Extensions of Measures.- 8 Measures Taking Infinite Values.- 9 Lebesgue Measure of Bounded Linear Sets.- 10 Lebesgue Measure on the Real Line.- 11 Lebesgue Measure in the N-Dimensional EuclideanlS²