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Hilbert Spaces

  • Ole ChristensenEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Hilbert spaces can be considered as infinite-dimensional analogues of \(\mathbb R^n\) and \(\mathbb C^n\): in fact, the structure imposed on Hilbert spaces imply that many of the properties of \(\mathbb R^n\) and \(\mathbb C^n\) (and the ways to deal with them) can be extended to Hilbert spaces. Most importantly, a Hilbert space is equipped with an inner product and an associated norm that makes the Hilbert space a Banach space.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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