Topological Vector Spaces, Distributions and Kernels / Francois Treves

Cover; Title Page; Copyright Page; Preface; Contents; Part I. Topological Vector Spaces. Spaces of Functions; 1. Filters. Topological Spaces. Continuous Mappings; 2. Vector Spaces. Linear Mappings; 3. Topological Vector Spaces. Definition; 4. Hausdorff Topological Vector Spaces. Quotient Topological Vector Spaces. Continuous Linear Mappings; Hausdorff Topological Vector Spaces; Quotient Topological Vector Spaces; Continuous Linear Mappings; 5. Cauchy Filters. Complete Subsets. Completion; 6. Compact Sets; 7. Locally Convex Spaces. Seminorms; 8. Metrizable Topological Vector Spaces. 29. Fourier Transforms of Distributions with Compact Support. The Paley-Wiener Theorem30. Fourier Transforms of Convolutions and Multiplications; 31. The Sobolev Spaces; 32. Equicontinuous Sets of Linear Mappings; 33. Barreled Spaces. The Banach-Steinhaus Theorem; 34. Applications of the Banach-Steinhaus Theorem; 34.1. Application to Hilbert Spaces; 34.2. Application to Separately Continuous Functions on Products; 34.3. Complete Subsets of LG(E; F); 34.4. Duals of Montel Spaces; 35. Further Study of the Weak Topology

This text for upper-level undergraduates and graduate students focuses on key notions and results in functional analysis. Extending beyond the boundaries of Hilbert and Banach space theory, it explores aspects of analysis relevant to the solution of partial differential equations. It features basic classical results, plus 390 exercises. 1967 edition