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1.

図書
図書
1. Function theory in the unit ball of C[n] (: us ; : gw)
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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2.

図書
図書
2. New constructions of functions holomorphic in the unit ball of C [italic superscript n]
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
3.

図書
図書
3. Real and complex analysis. 3rd ed
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：
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