Real and Functional Analysis - Lang, Serge
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This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters. …mehr

Produktbeschreibung
This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.
  • Produktdetails
  • Graduate Texts in Mathematics .142
  • Verlag: Springer New York / Springer, Berlin
  • 3. Aufl.
  • Seitenzahl: 600
  • Erscheinungstermin: 23. Oktober 2012
  • Englisch
  • Abmessung: 235mm x 155mm x 32mm
  • Gewicht: 890g
  • ISBN-13: 9781461269380
  • ISBN-10: 1461269385
  • Artikelnr.: 39503903
Inhaltsangabe
I Sets.- II Topological Spaces.- III Continuous Functions on Compact Sets.- IV Banach Spaces.- V Hilbert Space.- VI The General Integral.- VII Duality and Representation Theorems.- VIII Some Applications of Integration.- IX Integration and Measures on Locally Compact Spaces.- X Riemann-Stieltjes Integral and Measure.- XI Distributions.- XII Integration on Locally Compact Groups.- XIII Differential Calculus.- XIV Inverse Mappings and Differential Equations.- XV The Open Mapping Theorem, Factor Spaces, and Duality.- XVI The Spectrum.- XVII Compact and Fredholm Operators.- XVIII Spectral Theorem for Bounded Hermltian Operators.- XIX Further Spectral Theorems.- XX Spectral Measures.- XXI Local Integration off Differential Forms.- XXII Manifolds.- XXIII Integration and Measures on Manifolds.- Table of Notation.