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1.

図書

図書
Walter Rudin
出版情報: New York : McGraw-Hill , Tokyo : Kogakusha, c1953  ix, 227 p. ; 21 cm
シリーズ名: International series in pure and applied mathematics
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2.

図書

図書
W.ルディン著 ; 近藤基吉, 柳原二郎共訳
出版情報: 東京 : 共立出版, 1971.4  4, 4, 306, 7p ; 22cm
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3.

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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目次情報: 続きを見る
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:
4.

図書

図書
Walter Rudin
出版情報: Providence, R.I. : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1986  xvi, 78 p. ; 26 cm
シリーズ名: Regional conference series in mathematics ; no. 63
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目次情報: 続きを見る
The pathology of inner functions $RW$-sequences Approximation by $E$-polynomials
The existence of inner functions Radial limits and singular measures $E$-functions in the Smirnov class Almost semicontinuous functions and $\tilde{A}(B)$ $
Approximation in $L^{1/2}$ The $L^1$-modification theorem Approximation by inner functions
The LSC property of $H^\infty$ Max-sets and nonapproximation theorems Inner maps
A Lusin-type theorem for $A(B)$ Continuity on open sets of full measure Composition with inner functions
The closure of $A(B)$ in $(LH)^p(B)$ Open problems
Bounded bases in $H^2(B)$ / Appendix I:
RW-sequences revisited / Appendix II:
References
The pathology of inner functions $RW$-sequences Approximation by $E$-polynomials
The existence of inner functions Radial limits and singular measures $E$-functions in the Smirnov class Almost semicontinuous functions and $\tilde{A}(B)$ $
Approximation in $L^{1/2}$ The $L^1$-modification theorem Approximation by inner functions
5.

図書

図書
Walter Rudin
出版情報: New York ; Berlin : Springer-Verlag, c1980  xiii, 436 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 241
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6.

図書

図書
Walter Rudin
出版情報: New York : Interscience Publishers, c1962  ix, 285 p. ; 24 cm
シリーズ名: Interscience tracts in pure and applied mathematics ; no. 12
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目次情報: 続きを見る
The Basic Theorems of Fourier Analysis
The Structure of Locally Compact Abelian Groups
Idempotent Measures
Homomorphisms of Group Algebras
Measures and Fourier Transforms on Thin Sets
Functions of Fourier Transforms
Closed Ideals in L?1(G)
Fourier Analysis on Ordered Groups
Closed Subalgebras of L?1(G)
Appendices: Topology, Topological Groups, Banach Spaces, Banach Algebras, Measure Theory
Bibliography
List of Special Symbols
Index
The Basic Theorems of Fourier Analysis
The Structure of Locally Compact Abelian Groups
Idempotent Measures
7.

図書

図書
Walter Rudin
出版情報: New York : W.A. Benjamin, 1969  188 p. ; 24 cm
シリーズ名: Mathematics lecture note series
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8.

図書

図書
Walter Rudin
出版情報: Tokyo : McGraw-Hill Kogakusha, c1964  ix, 270 p. ; 21 cm
シリーズ名: International series in pure and applied mathematics
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9.

図書

図書
Walter Rudin
出版情報: New York : McGraw-Hill, c1966  xi, 412 p. ; 24 cm
シリーズ名: McGraw-Hill series in higher mathematics
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10.

図書

図書
Walter Rudin
出版情報: New Delhi : Tata McGraw-Hill, 1974  xii, 452 p. ; 23 cm
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