On the Abstract Subordinated Exit Equation
Let ℙ=(𝑃𝑡)𝑡>0 be a 𝐶0-contraction semigroup on a real Banach space ℬ. A ℙ-exit law is a ℬ-valued function 𝑡∈]0,∞[→𝜑𝑡∈ℬ satisfying the functional equation: 𝑃𝑡𝜑𝑠=𝜑𝑡+𝑠, 𝑠,𝑡>0. Let 𝛽 be a Bochner subordinator and let ℙ𝛽 be the subordinated semigroup of ℙ (in the Bochner sense) by means of 𝛽. Under...
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Hindawi Limited
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/390218 |
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doaj-84444605eeba4f7aa4704a1fd789d1622020-11-24T20:54:10ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/390218390218On the Abstract Subordinated Exit EquationHassen Mejri0Ezzedine Mliki1Institut Supérieur d'Informatique et des Technologie de Communication de Hammam Sousse, 4011-G.P.1 Sousse, TunisiaInstitut Préparatoire aux Études d'Ingénieurs de Monastir, 5000 Monastir, TunisiaLet ℙ=(𝑃𝑡)𝑡>0 be a 𝐶0-contraction semigroup on a real Banach space ℬ. A ℙ-exit law is a ℬ-valued function 𝑡∈]0,∞[→𝜑𝑡∈ℬ satisfying the functional equation: 𝑃𝑡𝜑𝑠=𝜑𝑡+𝑠, 𝑠,𝑡>0. Let 𝛽 be a Bochner subordinator and let ℙ𝛽 be the subordinated semigroup of ℙ (in the Bochner sense) by means of 𝛽. Under some regularity assumption, it is proved in this paper that each ℙ𝛽-exit law is subordinated to a unique ℙ-exit law.http://dx.doi.org/10.1155/2010/390218 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hassen Mejri Ezzedine Mliki |
| spellingShingle |
Hassen Mejri Ezzedine Mliki On the Abstract Subordinated Exit Equation Abstract and Applied Analysis |
| author_facet |
Hassen Mejri Ezzedine Mliki |
| author_sort |
Hassen Mejri |
| title |
On the Abstract Subordinated Exit Equation |
| title_short |
On the Abstract Subordinated Exit Equation |
| title_full |
On the Abstract Subordinated Exit Equation |
| title_fullStr |
On the Abstract Subordinated Exit Equation |
| title_full_unstemmed |
On the Abstract Subordinated Exit Equation |
| title_sort |
on the abstract subordinated exit equation |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2010-01-01 |
| description |
Let ℙ=(𝑃𝑡)𝑡>0 be a 𝐶0-contraction semigroup on a real Banach space ℬ. A ℙ-exit law is a ℬ-valued function 𝑡∈]0,∞[→𝜑𝑡∈ℬ satisfying the functional equation: 𝑃𝑡𝜑𝑠=𝜑𝑡+𝑠, 𝑠,𝑡>0. Let 𝛽 be a Bochner subordinator and let ℙ𝛽 be the subordinated semigroup of ℙ (in the Bochner sense) by means of 𝛽. Under some regularity assumption, it is proved in this paper that each ℙ𝛽-exit law is subordinated to a unique ℙ-exit law. |
| url |
http://dx.doi.org/10.1155/2010/390218 |
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AT hassenmejri ontheabstractsubordinatedexitequation AT ezzedinemliki ontheabstractsubordinatedexitequation |
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