For a $n\times n$ polynomial matrix $M$ and a linear operator $A$ on some Banach space $E$ we previously defined the polynomial operator matrix $\sA :=M(A)$ on the product space $\sE :=E^n$, but needed quite strong conditions on $M$ and $A$ to ensure that $\sA$ is the generator of a strongly continuous semigroup on $\sE$. In this paper we will show that it is possible to find a restriction $\sAG$ of $\sA$ to an abstract ``energy space" $\sEG$ such that $\sAG$ is a generator on $\sEG$ under much less restrictive assumptions on $M$ and $A$.

CAUCHY-PROBLEMS FOR POLYNOMIAL OPERATOR MATRICES ON ABSTRACT ENERGY SPACES

ENGEL, KLAUS JOCHEN OTTO;
1990-01-01

Abstract

For a $n\times n$ polynomial matrix $M$ and a linear operator $A$ on some Banach space $E$ we previously defined the polynomial operator matrix $\sA :=M(A)$ on the product space $\sE :=E^n$, but needed quite strong conditions on $M$ and $A$ to ensure that $\sA$ is the generator of a strongly continuous semigroup on $\sE$. In this paper we will show that it is possible to find a restriction $\sAG$ of $\sA$ to an abstract ``energy space" $\sEG$ such that $\sAG$ is a generator on $\sEG$ under much less restrictive assumptions on $M$ and $A$.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/17265
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 2
social impact