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Toeplitz operator : ウィキペディア英語版
Toeplitz operator

In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space.
== Details ==

Let ''S''1 be the circle, with the standard Lebesgue measure, and ''L''2(''S''1) be the Hilbert space of square-integrable functions. A bounded measurable function ''g'' on ''S''1 defines a multiplication operator ''Mg'' on ''L''2(''S''1). Let ''P'' be the projection from ''L''2(''S''1) onto the Hardy space ''H''2. The ''Toeplitz operator with symbol g'' is defined by
:T_g = P M_g \vert_,
where " | " means restriction.
A bounded operator on ''H''2 is Toeplitz if and only if its matrix representation, in the basis , has constant diagonals.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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