Topological vector spaces, distributions and kernels [[electronic resource] /] / François Treves

• Autore: Treves Francois <1930->
• Pubblicazione: New York, : Academic Press, 1967
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (583 p.)
• Disciplina: 515
• Soggetto topico: Functional analysis; Linear topological spaces
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographies and index.
• Nota di contenuto: 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 ; 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 ; 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) ; 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 ; 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 ; Chapter 33. Barreled Spaces. The Banach-Steinhaus Theorem
• Sommario/riassunto: Topological vector spaces, distributions and kernels
• Titolo autorizzato: Topological, vector spaces, distributions and kernels
• ISBN: 1-281-76763-8; 9786611767631; 0-08-087337-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910782597603321
• Lo trovi qui: Univ. Federico II
• Serie: Pure and applied mathematics (Academic Press) ; ; 25.