Real and complex analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
McGraw-Hill
1986
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| Ausgabe: | 3. ed. |
| Schriftenreihe: | McGraw-Hill international editions : Mathematics series.
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 416 S. |
| ISBN: | 0070542341 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804116510761811968 |
|---|---|
| adam_text | Titel: Real and complex analysis
Autor: Rudin, Walter
Jahr: 1986
CONTENTS Preface xiii Prologue: The Exponential Function l Chapter 1 Abstract Integration 5 Set-theoretic notations and terminology 6 The concept of measurability 8 Simple functions 15 Elementary properties of measures 16 Arithmetic in [0, oo] 18 Integration of positive functions 19 Integration of complex functions 24 The role played by sets of measure zero 27 Exercises 31 Chapter 2 Positive Borel Measures 33 Vector spaces 33 Topological preliminaries 35 The Riesz representation theorem 40 Regularity properties of Borel measures 47 Lebesgue measure 49 Continuity properties of measurable functions 55 Exercises 57 Chapter 3 //-Spaces 61 Convex functions and inequalities 61 The //-spaces 65 Approximation by continuous functions 69 Exercises 71 via
76 76 82 88 92 95 95 97 100 103 104 108 112 116 116 120 124 126 129 132 135 135 144 150 156 160 160 163 164 167 170 172 174 178 178 180 185 190 193 Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Examples of Banach Space Techniques Banach spaces Consequences of Baire’s theorem Fourier series of continuous functions Fourier coefficients of L -functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on U The Riesz representation theorem Exercises Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L 1 Exercises
s ix 196 196 200 204 208 214 217 224 227 231 231 233 237 239 245 249 253 253 254 256 260 262 264 266 266 270 273 274 276 278 278 279 281 282 285 289 291 293 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 Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Approximation by Rational Functions Preparation Runge’s theorem The Mittag-Leffler theorem Simply connected regions Exercises Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class £f Continuity at the boundary Conformal mapping of an annulus Exercises
298 298 301 304 307 310 312 315 319 319 323 326 328 331 332 335 335 337 341 342 346 350 352 356 356 357 362 365 369 371 371 372 377 380 383 386 386 387 390 394 Zeros of Holomorphic Functions Infinite products The Weierstrass factorization theorem An interpolation problem Jensen’s formula Blaschke products The Miintz-Szasz theorem Exercises Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises H p - Spaces Subharmonic functions The spaces H p and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analyiic classes The Denjoy-Carleman theorem Exercises Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan’s theorem Exercises
CONTENTS XI Appendix: Hausdorif’s Maximality Theorem 395 Notes and Comments 397 Bibliography 405 List of Special Symbols 407 Index 409
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| author | Rudin, Walter 1921-2010 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
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| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| spelling | Rudin, Walter 1921-2010 Verfasser (DE-588)119445670 aut Real and complex analysis 3. ed. New York u.a. McGraw-Hill 1986 XIV, 416 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill international editions : Mathematics series. Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 Analysis (DE-588)4001865-9 s Reelle Analysis (DE-588)4627581-2 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001347573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Real and complex analysis |
| title_auth | Real and complex analysis |
| title_exact_search | Real and complex analysis |
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| title_fullStr | Real and complex analysis |
| title_full_unstemmed | Real and complex analysis |
| title_short | Real and complex analysis |
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| topic | Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd Analysis (DE-588)4001865-9 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Mathematical analysis Reelle Analysis Analysis Funktionentheorie Lehrbuch |
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