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| Generalized Semigroup on(V, H, a) |
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Citation： |
Yao Yunlong.Generalized Semigroup on(V, H, a)[J].Chinese Annals of Mathematics B,1985,6(1):27~34 |
| Page view： 953
Net amount： 853 |
Authors： |
Yao Yunlong; |
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| Abstract： |
Let V and H be two Hilbert spaces satisfying the imbedding relation V\subset H. Let $[ - \mathscr{A}:V \to V'\]$ be the linear operator determined by a(u, v) = <\mathscr{A}u, v> for u, v\in V, where a(u, v) is a continuous sesquilinear form on V satisfying
$a(u, u)+\lambda|u|_H^2\geq c||u||_V^2$
for u\in V and some \lambda \in R and c>0.
In this paper it is proved that —\mathscr{A} is the generator of an analytic C_0-semigroup on V'. Furthermore, if b(u, v) is a continuous sesquilinear form on HxV and \mathscr{B}: H\rightarrow V, the linear operator determined by b(u, v) = (\mathscr{B}u, v) for u, v\in V, then —\mathscr{A}—mathscr{B} is also the generator of C_0-semigroup on V'.
Also, similar results are proved on “inserted” spaces V_\theta(\theta \geq -1) which are determined by the spectrum system of \mathscr{A}. |
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