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1.

図書

図書
Walter Rudin
出版情報: New York : McGraw-Hill, c1973  xiii, 397 p. ; 24 cm
シリーズ名: McGraw-Hill series in higher mathematics
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Preface
General Theory / Part 1:
Topological Vector Space Introduction Separation properties Linear Mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises / 1:
Completeness Baire category The Banach-Steinhaus theorem The open mapping theorem The closed graph theorem Bilinear mappings Exercises / 2:
Convexity The Hahn-Banach theorems Weak topologies Compact convex sets Vector-valued integration Holomorphic functions Exercises / 3:
Duality in Banach Spaces The normed dual of a normed space Adjoints Compact operators Exercises / 4:
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 / 5:
Distributions and Fourier Transforms / Part 2:
Test Functions and Distributions Introduction Test function spaces Calculus with distributions Localization Supports of distributions Distributions as derivatives Convolutions Exercises / 6:
Fourier Transforms Basic properties Tempered distributions Paley-Wiener theorems Sobolev's lemma Exercises / 7:
Applications to Differential Equations Fundamental solutions Elliptic equations Exercises / 8:
Tauberian Theory Wiener's theorem The prime number theorem The renewal equation Exercises / 9:
Banach Algebras and Spectral Theory / Part 3:
Banach Algebras Introduction Complex homomorphisms Basic properties of spectra Symbolic calculus The group of invertible elements Lomonosov's invariant subspace theorem Exercises / 10:
Commutative Banach Algebras Ideals and homomorphisms Gelfand transforms Involutions Applications to noncommutative algebras Positive functionals Exercises / 11:
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 / 12:
Unbounded Operators Introduction Graphs and symmetric operators The Cayley transform Resolutions of the identity The spectral theorem Semigroups of operators Exercises / 13:
Compactness and Continuity / Appendix A:
Notes and Comments / Appendix B:
Bibliography List of Special Symbols
Index
Preface
General Theory / Part 1:
Topological Vector Space Introduction Separation properties Linear Mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises / 1:
2.

図書

図書
[by] Edward J. Beltrami
出版情報: New York : Academic Press, 1970  xiv, 235 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 63
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3.

図書

図書
Henry Hermes, Joseph P. LaSalle
出版情報: New York : Academic Press, 1969  viii, 136 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 56
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4.

図書

図書
A.H. Zemanian
出版情報: New York : Academic Press, 1972  xv, 231 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 97
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