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EnglishMany systems of linear evolution equations can be written as a single equation $$\dot u(t)=\s A u(t),\eqno(*)$$ where $u$ is a function with values in a product space $E^n$ and $\s A =(A_{ij})_{n\times n}$ is a matrix whose entries $A_{ij}$ are linear operators on $E$. In order to prove the well-posedness of $(*)$ one shows that $\s A$ generates a strongly continuous semigroup on $E^n$. In this paper we consider the case where the $A_{ij}$ are polynomials $p_{ij}(A)$ with respect to a single (unbounded) operator $A$ on $E$ and restrict our attention to the case of $2\times2$ matrices.
http://hdl.handle.net/11697/10375| Titolo: | POLYNOMIAL OPERATOR MATRICES AS SEMIGROUP GENERATORS - THE 2X2 CASE |
| Autori interni: | ENGEL, KLAUS JOCHEN OTTO |
| Data di pubblicazione: | 1989 |
| Rivista: | MATHEMATISCHE ANNALEN |
| Abstract: | Many systems of linear evolution equations can be written as a single equation $$\dot u(t)=\s A u(t),\eqno(*)$$ where $u$ is a function with values in a product space $E^n$ and $\s A =(A_{ij})_{n\times n}$ is a matrix whose entries $A_{ij}$ are linear operators on $E$. In order to prove the well-posedness of $(*)$ one shows that $\s A$ generates a strongly continuous semigroup on $E^n$. In this paper we consider the case where the $A_{ij}$ are polynomials $p_{ij}(A)$ with respect to a single (unbounded) operator $A$ on $E$ and restrict our attention to the case of $2\times2$ matrices. |
| Handle: | http://hdl.handle.net/11697/10375 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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