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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Christensen, O. (2010). Hilbert Spaces. In: Functions, Spaces, and Expansions. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4980-7_4
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DOI: https://doi.org/10.1007/978-0-8176-4980-7_4
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4979-1
Online ISBN: 978-0-8176-4980-7
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