TY  - BOOK
AU  - A A Kirillov
AU  - A A Kirillov.
TI  - Theorems and problems in functional analysis
SN  - 9781461381556
U1  - 515.7 KIR 
PY  - 1982///
CY  - New York 
PB  - : Springer-Verlag
KW  - Mathematics
KW  - Functional analysis
KW  - Algebra
KW  - A A Kirillov
N1  - 	Theory.- I Concepts from Set Theory and Topology.- 1. Relations. The Axiom of Choice and Zorn's Lemma.- 2. Completions.- 3. Categories and Functors.- II Theory of Measures and Integrals..- 1. Measure Theory.- 1. Algebras of Sets.- 2. Extension of a Measure.- 3. Constructions of Measures.- 2. Measurable Functions.- 1. Properties of Measurable Functions.- 2. Convergence of Measurable Functions.- 3. Integrals.- 1. The Lebesgue Integral.- 2. Functions of Bounded Variation and the Lebesque-Stieltjes Integral.- 3. Properties of the Lebesgue Integral.- III Linear Topological Spaces and Linear Operators.- 1. General Theory.- 1. Topology, Convexity, and Seminorms.- 2. Dual Spaces.- 3. The Hahn-Banach Theorem.- 4. Banach Spaces.- 2. Linear Operators.- 1. The Space of Linear Operators.- 2. Compact Sets and Compact Operators.- 3. The Theory of Fredholm Operators.- 3. Function Spaces and Generalized Functions.- 1. Spaces of Integrable Functions.- 2. Spaces of Continuous Functions.- 3. Spaces of Smooth Functions.- 4. Generalized Functions.- 5. Operations on Generalized Functions.- 4. Hilbert Spaces.- 1. The Geometry of Hilbert Spaces.- 2. Operators on a Hilbert Space.- IV The Fourier Transformation and Elements of Harmonic Analysis.- 1. Convolutions on an Abelian Group.- 1. Convolutions of Test Functions.- 2. Convolutions of Generalized Functions.- 2. The Fourier Transformation.- 1. Characters on an Abelian Group.- 2. Fourier Series.- 3. The Fourier Integral.- 4. Fourier Transformation of Generalized Functions.- V The Spectral Theory of Operators.- 1. The Functional Calculus.- 1. Functions of Operators in a Finite-Dimensional Space..- 2. Functions of Bounded Selfadjoint Operators.- 3. Unbounded Selfadjoint Operators.- 2. Spectral Decomposition of Operators.- 1. Reduction of an Operator to the Form of Multiplication by a Function.- 2. The Spectral Theorem.- Problems.- I Concepts from Set Theory and Topology.- 1. Relations. The Axiom of Choice and Zorn's Lemma.- 2. Completions.- 3. Categories and Functors.- II Theory of Measures and Integrals..- 1. Measure Theory.- 1. Algebras of Sets.- 2. Extension of a Measure.- 3. Constructions of Measures.- 2. Measurable Functions.- 1. Properties of Measurable Functions.- 2. Convergence of Measurable Functions.- 3. Integrals.- 1. The Lebesgue Integral.- 2. Functions of Bounded Variation and the Lebesque-Stieltjes Integral.- 3. Properties of the Lebesgue Integral.- III Linear Topological Spaces and Linear Operators.- 1. General Theory.- 1. Topology, Convexity, and Seminorms.- 2. Dual Spaces.- 3. The Hahn-Banach Theorem.- 4. Banach Spaces.- 2. Linear Operators.- 1. The Space of Linear Operators.- 2. Compact Sets and Compact Operators.- 3. The Theory of Fredholm Operators.- 3. Function Spaces and Generalized Functions.- 1. Spaces of Integrable Functions.- 2. Spaces of Continuous Functions.- 3. Spaces of Smooth Functions.- 4. Generalized Functions.- 5. Operations on Generalized Functions.- 4. Hilbert Spaces.- 1. The Geometry of Hilbert Spaces.- 2. Operators on a Hilbert Space.- IV The Fourier Transformation and Elements of Harmonic Analysis.- 1. Convolutions on an Abelian Group.- 1. Convolutions of Test Functions.- 2. Convolutions of Generalized Functions.- 2. The Fourier Transformation.- 1. Characters on an Abelian Group.- 2. Fourier Series.- 3. The Fourier Integral.- 4. Fourier Transformation of Generalized Functions.- V The Spectral Theory of Operators.- 1. The Functional Calculus.- 1. Functions of Operators in a Finite-Dimensional Space..- 2. Functions of Bounded Selfadjoint Operators.- 3. Unbounded Selfadjoint Operators.- 2. Spectral Decomposition of Operators.- 1. Reduction of an Operator to the Form of Multiplication by a Function.- 2. The Spectral Theorem.- Hints.- I Concepts from Set Theory and Topology.- 1. Relations. The Axiom of Choice and Zorn's Lemma.- 2. Completions.- 3. Categories and Functors.- II Theory of Measures and Integrals..- 1. Measure Theory.- 1. Algebras of Sets.- 2. Extension of a Measure.- 3. Constructions of Measures.- 2. Measurable Functions.- 1. Properties of Measurable Functions.- 2. Convergence of Measurable Functions.- 3. Integrals.- 1. The Lebesgue Integral.- 2. Functions of Bounded Variation and the Lebesque-Stieltjes Integral.- 3. Properties of the Lebesgue Integral.- III Linear Topological Spaces and Linear Operators.- 1. General Theory.- 1. Topology, Convexity, and Seminorms.- 2. Dual Spaces.- 3. The Hahn-Banach Theorem.- 4. Banach Spaces.- 2. Linear Operators.- 1. The Space of Linear Operators.- 2. Compact Sets and Compact Operators.- 3. The Theory of Fredholm Operators.- 3. Function Spaces and Generalized Functions.- 1. Spaces of Integrable Functions.- 2. Spaces of Continuous Functions.- 3. Spaces of Smooth Functions.- 4. Generalized Functions.- 5. Operations on Generalized Functions.- 4. Hilbert Spaces.- 1. The Geometry of Hilbert Spaces.- 2. Operators on a Hilbert Space.- IV The Fourier Transformation and Elements of Harmonic Analysis.- 1. Convolutions on an Abelian Group.- 1. Convolutions of Test Functions.- 2. Convolutions of Generalized Functions.- 2. The Fourier Transformation.- 1. Characters on an Abelian Group.- 2. Fourier Series.- 3. The Fourier Integral.- 4. Fourier Transformation of Generalized Functions.- V The Spectral Theory of Operators.- 1. The Functional Calculus.- 1. Functions of Operators in a Finite-Dimensional Space..- 2. Functions of Bounded Selfadjoint Operators.- 3. Unbounded Selfadjoint Operators.- 2. Spectral Decomposition of Operators.- 1. Reduction of an Operator to the Form of Multiplication by a Function.- 2. The Spectral Theorem.- List of Notation
N2  - Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on
ER  -