History of Hilbert space

	Revision 11 . . December 12, 2001 2:34 am by AxelBoldt [Some context.]
	Revision 10 . . (edit) December 12, 2001 1:22 am by Taw [format fix]
	Revision 9 . . (edit) December 12, 2001 1:20 am by Taw [format fix]
	Revision 8 . . (edit) November 3, 2001 5:29 am by (logged).95.173.xxx

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A Hilbert space H is an inner product space which is complete with respect to the norm defined by the inner product (and is hence a Banach space). Hilbert spaces were named after David Hilbert, who studied them in the context of integral equations. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion, certain linear transformations such as the Fourier transform, and are of crucial importance in the mathematical formulation of quantum mechanics.

A Hilbert space is an inner product space which is complete with respect to the norm defined by the inner product (and is hence a Banach space). Hilbert spaces were named after David Hilbert, who studied them in the context of integral equations. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion, certain linear transformations such as the Fourier transform, and are of crucial importance in the mathematical formulation of quantum mechanics. Hilbert spaces are studied in the branch of mathematics called functional analysis.