In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general case being called the Feller–Miyadera–Phillips theorem (after William Feller, Isao Miyadera, and Ralph Phillips). The contraction semigroup case is widely used in the theory of Markov processes. In other scenarios, the closely related Lumer–Phillips theorem is often more useful in determining whether a given operator generates a strongly continuous contraction semigroup. The theorem is named after the mathematicians Einar Hille and Kōsaku Yosida who independently discovered the result around 1948.
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| - Satz von Hille-Yosida (de)
- Théorème de Hille-Yosida (fr)
- Hille–Yosida theorem (en)
- Teorema di Hille-Yosida (it)
- ヒレ–吉田の定理 (ja)
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| - In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general case being called the Feller–Miyadera–Phillips theorem (after William Feller, Isao Miyadera, and Ralph Phillips). The contraction semigroup case is widely used in the theory of Markov processes. In other scenarios, the closely related Lumer–Phillips theorem is often more useful in determining whether a given operator generates a strongly continuous contraction semigroup. The theorem is named after the mathematicians Einar Hille and Kōsaku Yosida who independently discovered the result around 1948. (en)
- En théorie des semi-groupes, le théorème de Hille-Yosida est un outil puissant et fondamental reliant les propriétés de dissipation de l'énergie d'un opérateur non borné à l'existence et l'unicité et la régularité des solutions d'une équation différentielle (E) . Ce résultat permet notamment de donner l'existence, l'unicité et la régularité des solutions d'une équation aux dérivées partielles plus efficacement que le théorème de Cauchy-Lipschitz-Picard, plus adapté aux équations différentielles ordinaires. (fr)
- 数学の関数解析学の分野におけるヒレ–吉田の定理（ヒレ–よしだのていり、英: Hille–Yosida theorem）とは、バナッハ空間上の線形作用素からなる強連続1パラメータ半群の生成素を特徴づける定理である。しばしば特別な場合として縮小半群のために適用され、また、一般的な場合としてフェラー-宮寺-フィリップスの定理（、宮寺功、ラルフ・フィリップスの名にちなむ）と呼ばれる定理が存在する。縮小半群の場合は、マルコフ過程の理論において広く研究されている。その他の場面では、この定理と関係の深いルーマー–フィリップスの定理が、「与えられた作用素が強連続な縮小半群を生成するかどうか」を見極める上で有用となる。ヒレ-吉田の定理は数学者のと吉田耕作の名にちなみ、1948年前後の彼らの研究によってそれぞれ独立に発見された。 (ja)
- In analisi funzionale, il teorema di Hille-Yosida caratterizza i generatori di semigruppi a un parametro fortemente continui di operatori lineari su spazi di Banach. A volte viene indicato per il caso speciale dei semigruppi di contrazione, con il caso generale che viene chiamato il teorema di Feller-Miyadera-Phillips (da William Feller, Isao Miyadera e Ralph Phillips). Il caso del semigruppo di contrazione è ampiamente usato nella teoria dei processi di Markov. In altri scenari, il teorema di Lumer-Phillips strettamente correlato è spesso più utile nel determinare se un dato operatore genera un semigruppo di contrazione fortemente continuo. Il teorema prende il nome dai matematici Einar Hille e Kōsaku Yosida che scoprirono indipendentemente il risultato intorno al 1948. (it)
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| - In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general case being called the Feller–Miyadera–Phillips theorem (after William Feller, Isao Miyadera, and Ralph Phillips). The contraction semigroup case is widely used in the theory of Markov processes. In other scenarios, the closely related Lumer–Phillips theorem is often more useful in determining whether a given operator generates a strongly continuous contraction semigroup. The theorem is named after the mathematicians Einar Hille and Kōsaku Yosida who independently discovered the result around 1948. (en)
- En théorie des semi-groupes, le théorème de Hille-Yosida est un outil puissant et fondamental reliant les propriétés de dissipation de l'énergie d'un opérateur non borné à l'existence et l'unicité et la régularité des solutions d'une équation différentielle (E) . Ce résultat permet notamment de donner l'existence, l'unicité et la régularité des solutions d'une équation aux dérivées partielles plus efficacement que le théorème de Cauchy-Lipschitz-Picard, plus adapté aux équations différentielles ordinaires. (fr)
- 数学の関数解析学の分野におけるヒレ–吉田の定理（ヒレ–よしだのていり、英: Hille–Yosida theorem）とは、バナッハ空間上の線形作用素からなる強連続1パラメータ半群の生成素を特徴づける定理である。しばしば特別な場合として縮小半群のために適用され、また、一般的な場合としてフェラー-宮寺-フィリップスの定理（、宮寺功、ラルフ・フィリップスの名にちなむ）と呼ばれる定理が存在する。縮小半群の場合は、マルコフ過程の理論において広く研究されている。その他の場面では、この定理と関係の深いルーマー–フィリップスの定理が、「与えられた作用素が強連続な縮小半群を生成するかどうか」を見極める上で有用となる。ヒレ-吉田の定理は数学者のと吉田耕作の名にちなみ、1948年前後の彼らの研究によってそれぞれ独立に発見された。 (ja)
- In analisi funzionale, il teorema di Hille-Yosida caratterizza i generatori di semigruppi a un parametro fortemente continui di operatori lineari su spazi di Banach. A volte viene indicato per il caso speciale dei semigruppi di contrazione, con il caso generale che viene chiamato il teorema di Feller-Miyadera-Phillips (da William Feller, Isao Miyadera e Ralph Phillips). Il caso del semigruppo di contrazione è ampiamente usato nella teoria dei processi di Markov. In altri scenari, il teorema di Lumer-Phillips strettamente correlato è spesso più utile nel determinare se un dato operatore genera un semigruppo di contrazione fortemente continuo. Il teorema prende il nome dai matematici Einar Hille e Kōsaku Yosida che scoprirono indipendentemente il risultato intorno al 1948. (it)
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