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Statements

Subject Item
dbr:Ornstein–Uhlenbeck_operator
dbo:wikiPageWikiLink
dbr:Dissipative_operator
Subject Item
dbr:Dissipative_operator
rdfs:label
Dissipativer Operator Dissipative operator 消散作用素
rdfs:comment
In mathematics, a dissipative operator is a linear operator A defined on a linear subspace D(A) of Banach space X, taking values in X such that for all λ > 0 and all x ∈ D(A) A couple of equivalent definitions are given below. A dissipative operator is called maximally dissipative if it is dissipative and for all λ > 0 the operator λI − A is surjective, meaning that the range when applied to the domain D is the whole of the space X. In der linearen Theorie sind dissipative Operatoren lineare Operatoren, die auf reellen oder komplexen Banachräumen definiert sind und gewisse Normabschätzungen erfüllen. Durch den Satz von Lumer-Phillips spielen sie eine wichtige Rolle bei der Betrachtung stark stetiger Halbgruppen. 数学における消散作用素（しょうさんさようそ、英: dissipative operator）とは、バナッハ空間 X に値を取り、すべての λ > 0 および x ∈ D(A) に対して が成立するような、X の線形部分空間 D(A) 上で定義される線形作用素 A のことを言う。消散作用素が極大消散（maximally dissipative）であるとは、すべての λ > 0 に対して作用素 λI − A が全射であることを言う。 極大消散作用素が縮小半群の生成素として特徴づけられるルーマー-フィリップスの定理において、消散作用素の概念は重要な役割を担う。
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dbo:abstract
In mathematics, a dissipative operator is a linear operator A defined on a linear subspace D(A) of Banach space X, taking values in X such that for all λ > 0 and all x ∈ D(A) A couple of equivalent definitions are given below. A dissipative operator is called maximally dissipative if it is dissipative and for all λ > 0 the operator λI − A is surjective, meaning that the range when applied to the domain D is the whole of the space X. An operator that obeys a similar condition but with a plus sign instead of a minus sign (that is, the negation of a dissipative operator) is called an accretive operator. The main importance of dissipative operators is their appearance in the Lumer–Phillips theorem which characterizes maximally dissipative operators as the generators of contraction semigroups. 数学における消散作用素（しょうさんさようそ、英: dissipative operator）とは、バナッハ空間 X に値を取り、すべての λ > 0 および x ∈ D(A) に対して が成立するような、X の線形部分空間 D(A) 上で定義される線形作用素 A のことを言う。消散作用素が極大消散（maximally dissipative）であるとは、すべての λ > 0 に対して作用素 λI − A が全射であることを言う。 極大消散作用素が縮小半群の生成素として特徴づけられるルーマー-フィリップスの定理において、消散作用素の概念は重要な役割を担う。 In der linearen Theorie sind dissipative Operatoren lineare Operatoren, die auf reellen oder komplexen Banachräumen definiert sind und gewisse Normabschätzungen erfüllen. Durch den Satz von Lumer-Phillips spielen sie eine wichtige Rolle bei der Betrachtung stark stetiger Halbgruppen.
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