UID:
almahu_9947367306502882
Format:
1 online resource (583 p.)
Edition:
2nd ed.
ISBN:
1-281-76763-8
,
9786611767631
,
0-08-087337-5
Series Statement:
Pure and applied mathematics ; 25
Content:
Topological vector spaces, distributions and kernels
Note:
Description based upon print version of record.
,
Front Cover; Topological Vector Spaces, Distributions and Kernels; Copyright Page; Contents; Preface; Part I: Topological Vector Spaces. Spaces of Functions; Chapter 1. Filters. Topological Spaces. Continuous Mappings; Chapter 2. Vector Spaces. Linear Mappings; Chapter 3. Topological Vector Spaces. Definition; Chapter 4. Hausdorff Topological Vector Spaces. Quotient Topological Vector Spaces. Continuous Linear Mappings; Hausdorff Topological Vector Spaces; Quotient Topological Vector Spaces; Continuous Linear Mappings; Chapter 5. Cauchy Filters. Complete Subsets. Completion
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Chapter 6. Compact SetsChapter 7. Locally Convex Spaces. Seminorms; Chapter 8. Metrizable Topological Vector Spaces; Chapter 9. Finite Dimensional Hausdorff Topological Vector Spaces. Linear Subspaces with Finite Codimension. Hyperplanes; Chapter 10. Fréchet Spaces. Examples; Example I. The Space of lk Functions in an Open Subset ? of Rn; Example II. The Space of Holomorphic Functions in an Open Subset ? of Cn; Example III. The Space of Formal Power Series in n Indeterminates; Example IV. The Space e of e8 Functions in Rn Rapidly Decreasing at Infinity
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Chapter 11. Normable Spaces. Banach Spaces. Examples.Chapter 12. Hilbert Spaces; Chapter 13. Spaces LF. Examples; Chapter 14. Bounded Sets; Chapter 15. Approximation Procedures in Spaces of Functions; Chapter 16. Partitions of Unity; Chapter 17. The Open Mapping Theorem; Part II: Duality. Spaces of Distributions; Chapter 18. The Hahn-Banach Theorem; (1) Problems of Approximation; (2) Problems of Existence; (3) Problems of Separation; Chapter 19. Topologies on the Dual; Chapter 20. Examples of Duals among Lp Spaces; Example I. The Duals of the Spaces of Sequences lp(1 = p 〈 + 8)
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Example II. The Duals of the Spaces Lp(?) (1 = p 〈 + 8)Chapter 21. Radon Measures. Distributions; Radon Measures in an Open Subset ? of Rn; Distributions in an Open Subset of Rn; Chapter 22. More Duals: Polynomials and Formal Power Series. Analytic Functionals; Polynomials and Formal Power Series; Analytic Functionals in an Open Subset ? of Cn; Chapter 23. Transpose of a Continuous Linear Map; Example I. Injections of Duals; Example II. Restrictions and Extensions; Example III. Differential Operators; Chapter 24. Support and Structure of a Distribution
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Distributions with Support at the OriginChapter 25.Example of Transpose: Fourier Transformation of Tempered Distributions; Chapter 26. Convolution of Functions; Chapter 27. Example of Transpose: Convolution of Distributions; Chapter 28. Approximation of Distributions by Cutting and Regularizing; Chapter 29. Fourier Transforms of Distributions with Compact Support The Paley-Wiener Theorem; Chapter 30. Fourier Transforms of Convolutions and Multiplications; Chapter 31. The Sobolev Spaces; Chapter 32. Equicontinuous Sets of Linear Mappings
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Chapter 33. Barreled Spaces. The Banach-Steinhaus Theorem
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English
Additional Edition:
ISBN 0-12-699450-1
Language:
English
