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In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory in the broad sense. They bring together the 'bound state' (eigenvector) and 'continuous spectrum', in one place. ==Motivation== A function such as the canonical homomorphism of the real line into the complex plane : is an eigenfunction of the differential operator : on the real line R, but isn't square-integrable for the usual Borel measure on R. To properly consider this function as an eigenfunction requires some way of stepping outside the strict confines of the Hilbert space theory. This was supplied by the apparatus of Schwartz distributions, and a ''generalized eigenfunction'' theory was developed in the years after 1950. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rigged Hilbert space」の詳細全文を読む スポンサード リンク
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