| 000 | 06584nam a22002177a 4500 | ||
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| 005 | 20181112155949.0 | ||
| 008 | 180404b xxu||||| |||| 00| 0 eng d | ||
| 020 | _a9781461381556 | ||
| 028 |
_aInternational Book Distributors _bFlat No.-17 , Prakash Apartment , 5 Ansari Road, Daryaganj , New Delhi. _c: 112024 _d: 23/03/2018 |
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| 082 | _a515.7 KIR | ||
| 100 |
_aA A Kirillov _a; A D Gvishiani. |
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| 245 |
_aTheorems and problems in functional analysis. _c/ A A Kirillov. |
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| 260 |
_aNew York _b: Springer-Verlag _c, ©1982. |
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| 300 |
_aix, 347 pages _b : illustrations _c; 24 cm. |
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| 365 | _b4736 | ||
| 505 | _a 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. | ||
| 520 | _aFunctional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. | ||
| 655 |
_aMathematics. _bFunctional analysis. _bAlgebra. _bA A Kirillov. |
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| 700 | _aA A Kirillov. | ||
| 942 | _cBOOK | ||
| 999 |
_c49302 _d49302 |
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