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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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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:
2.

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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3.

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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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
4.

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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5.

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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6.

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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7.

図書

図書
Walter Rudin
出版情報: New York ; Tokyo : McGraw-Hill, c1991  xv, 424 p. ; 24 cm
シリーズ名: International series in pure and applied mathematics
Churchill-Brown series
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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:
8.

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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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
9.

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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10.

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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11.

図書

図書
Walter Rudin
出版情報: New York ; London : McGraw-Hill, 1974  xii, 452 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 Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1:
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2:
L p -Spaces Convex functions and inequalities TheL p -spaces Approximation by continuous functions Exercises / Chapter 3:
Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises / Chapter 4:
Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients ofL1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises / Chapter 5:
Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals onL p The Riesz representation theorem Exercises / Chapter 6:
Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises / Chapter 7:
Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises / Chapter 8:
Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebraL1 Exercises / Chapter 9:
Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises / Chapter 10:
Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises / Chapter 11:
The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelouml;f method An interpolation theorem A converse of the maximum modulus theorem Exercises / Chapter 12:
Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises / Chapter 13:
Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The classL Continuity at the boundary Conformal mapping of an annulus Exercises / Chapter 14:
Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muuml;ntz-Szas theorem Exercises / Chapter 15:
Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises / Chapter 16:
H p -Spaces Subharmonic functions The spacesH p and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises / Chapter 17:
Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises / Chapter 18:
Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem / Chapter 19:
Preface Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1:
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2:
12.

図書

図書
Walter Rudin
出版情報: New York ; Tokyo : McGraw-Hill, c1987  xiv, 416 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 Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1:
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2:
L p -Spaces Convex functions and inequalities TheL p -spaces Approximation by continuous functions Exercises / Chapter 3:
Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises / Chapter 4:
Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients ofL1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises / Chapter 5:
Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals onL p The Riesz representation theorem Exercises / Chapter 6:
Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises / Chapter 7:
Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises / Chapter 8:
Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebraL1 Exercises / Chapter 9:
Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises / Chapter 10:
Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises / Chapter 11:
The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelouml;f method An interpolation theorem A converse of the maximum modulus theorem Exercises / Chapter 12:
Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises / Chapter 13:
Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The classL Continuity at the boundary Conformal mapping of an annulus Exercises / Chapter 14:
Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muuml;ntz-Szas theorem Exercises / Chapter 15:
Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises / Chapter 16:
H p -Spaces Subharmonic functions The spacesH p and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises / Chapter 17:
Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises / Chapter 18:
Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem / Chapter 19:
Preface Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1:
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2:
13.

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, 2010.12  4, 4, 306, 7p ; 22cm
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14.

図書

図書
Walter Rudin
出版情報: New York : McGraw-Hill, c1976  x, 342 p. ; 24 cm
シリーズ名: International series in pure and applied mathematics
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15.

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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