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Functional Analysis : Entering Hilbert Space - Vagn Lundsgaard Hansen

Functional Analysis

Entering Hilbert Space

By: Vagn Lundsgaard Hansen

eText | 18 May 2006

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This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.

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Non-FictionSciencePhysicsMathematicsCalculus & Mathematical AnalysisDifferential Calculus & Equations

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Hardcover

Published: 22nd May 2006

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