浙江广播电视大学校志[地方志]:1979-1995

Preface
General Theory
Topological Vector Space Introduction Separation properties Linear Mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises
Completeness Baire category The Banach-Steinhaus theorem The open mapping theorem The closed graph theorem Bilinear mappings Exercises
Convexity The Hahn-Banach theorems Weak topologies Compact convex sets Vector-valued integration Holomorphic functions Exercises
Duality in Banach Spaces The normed dual of a normed space Adjoints Compact operators Exercises
Some Applications A continuity theorem Closed subspaces ofL p -spaces The range of a vector-valued measure A generalized Stone-Weierstrass theorem Two interpolation theorems Kakutani's fixed point theorem Haar measure on compact groups Uncomplemented subspaces Sums of Poisson kernels Two more fixed point theorems Exercises
Distributions and Fourier Transforms
Test Functions and Distributions Introduction Test function spaces Calculus with distributions Localization Supports of distributions Distributions as derivatives Convolutions Exercises
Fourier Transforms Basic properties Tempered distributions Paley-Wiener theorems Sobolev's lemma Exercises
Applications to Differential Equations Fundamental solutions Elliptic equations Exercises
Tauberian Theory Wiener's theorem The prime number theorem The renewal equation Exercises
Banach Algebras and Spectral Theory
Banach Algebras Introduction Complex homomorphisms Basic properties of spectra Symbolic calculus The group of invertible elements Lomonosov's invariant subspace theorem Exercises
Commutative Banach Algebras Ideals and homomorphisms Gelfand transforms Involutions Applications to noncommutative algebras Positive functionals Exercises
Bounded Operators on a Hillbert Space Basic facts Bounded operators A commutativity theorem Resolutions of the identity The spectral theorem Eigenvalues of normal operators Positive operators and square roots The group of invertible operators A characterization of B*-algebras An ergodic theorem Exercises
Unbounded Operators Introduction Graphs and symmetric operators The Cayley transform Resolutions of the identity The spectral theorem Semigroups of operators Exercises
Compactness and Continuity
Notes and Comments
Bibliography List of Special Symbols
Index