Real and Functional Analysis (Graduate Texts in Mathematics, 142)

Lang, Serge

ISBN 10: 0387940014 / ISBN 13: 9780387940014

Editore: Springer, 1993

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Dati bibliografici

• Titolo: Real and Functional Analysis (Graduate Texts in Mathematics, 142)
• Editore: Springer
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0387940014
• ISBN 13: 9780387940014
• Rilegatura: Rilegato
• Edizione: terza edizione
• Condizione: New

Descrizione articolo

Riassunto

This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal­ ysis. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g.

Contenuti

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.