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2015-01-08T06:32:12Z

Dating maintenance tags: {{Unreferenced}}

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	~~In [[operator theory]], a '''Toeplitz operator'''~~ is ~~the [[dilation (operator theory)\|compression]] of a [[multiplication operator]] on the circle to the [[Hardy space]]~~.		Her name is Marti. As somebody what I like is mah jongg and I'll be starting something else along utilizing it. My job can be a customer service representative. Delaware is where her property is. Check out her website here: http://www.eolienne-siliken.fr/de-gros-nike-air-max-homme.html<br><br>my website [http://www.eolienne-siliken.fr/de-gros-nike-air-max-homme.html Nike Air Max Homme]

	~~== Details ==~~

	~~Let ''S''<sup>1</sup> be the circle, with the standard Lebesgue measure,~~ and '~~'L''<sup>2</sup>(''S''<sup>1</sup>)~~ be ~~the Hilbert space of square-integrable functions~~. ~~A bounded measurable function ''g'' on ''S''<sup>1</sup> defines~~ a ~~[[multiplication operator]] ''M<sub>g</sub>'' on ''L''<sup>2</sup>(''S''<sup>1</sup>)~~. ~~Let ''P'' be the projection from ''L''<sup>2</sup>(''S''<sup>1</sup>) onto the Hardy space ''H''<sup>2</sup>. The ''Toeplitz operator with symbol g''~~ is ~~defined by~~

	~~:<math>T_g = P M_g \vert_{H^2},</math>~~

	where ~~" \| " means restriction~~.

	~~A bounded operator on ''H''<sup>2<~~/~~sup> is Toeplitz if and only if its matrix representation, in the basis {''z<sup>n<~~/~~sup>'', ''n'' ≥ 0}, has constant diagonals.~~

	~~== References ==~~
	*{{citation\|last1=Böttcher\|first1=A.~~\|author1~~-~~link=Albrecht Böttcher\|last2=Silbermann\|first2=B~~.~~\|year=2006\|title=Analysis of Toeplitz Operators\|edition=2nd\|publisher=Springer~~-~~Verlag\|series=Springer Monographs in Mathematics\|isbn= 978~~-3-~~540~~-~~32434~~-~~8}}~~.
	*{{citation\|first1=Marvin\|last1=Rosenblum\|first2=James\|last2=Rovnyak\|title=Hardy Classes and Operator Theory\|year=1985\|publisher=Oxford University Press}}. ~~Reprinted by Dover Publications, 1997, ISBN 978~~-0-~~486~~-~~69536~~-5.

	~~{{DEFAULTSORT:Toeplitz Operator}}~~
	~~[[Category:Operator theory~~]]

	~~{{mathanalysis-stub}}~~

en>Pluma: /* Methods corresponding to particular algebraic groups */

2011-08-02T21:00:31Z

Methods corresponding to particular algebraic groups

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In [[operator theory]], a '''Toeplitz operator''' is the [[dilation (operator theory)|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

:<math>T_g = P M_g \vert_{H^2},</math>

where " | " means restriction.

A bounded operator on ''H''2 is Toeplitz if and only if its matrix representation, in the basis {''zn'', ''n'' ≥ 0}, has constant diagonals.

== References ==
*{{citation|last1=Böttcher|first1=A.|author1-link=Albrecht Böttcher|last2=Silbermann|first2=B.|year=2006|title=Analysis of Toeplitz Operators|edition=2nd|publisher=Springer-Verlag|series=Springer Monographs in Mathematics|isbn= 978-3-540-32434-8}}.
*{{citation|first1=Marvin|last1=Rosenblum|first2=James|last2=Rovnyak|title=Hardy Classes and Operator Theory|year=1985|publisher=Oxford University Press}}. Reprinted by Dover Publications, 1997, ISBN 978-0-486-69536-5.

{{DEFAULTSORT:Toeplitz Operator}}
[[Category:Operator theory]]

{{mathanalysis-stub}}

Algebraic-group factorisation algorithm - Revision history

en>AnomieBOT: Dating maintenance tags: {{Unreferenced}}

en>Pluma: /* Methods corresponding to particular algebraic groups */