排序方式: 共有14条查询结果,搜索用时 15 毫秒
1.
Analytic families of semigroups 总被引:1,自引:0,他引:1
Shmuel Kantorovitz 《Semigroup Forum》1997,54(1):356-363
The Cauchy Problem for linear partial differential equations with coefficients depending analytically on a parameter, motivates
the study of analytic families of infinitesimal generators of semigroups. The relations between the three natural ways to
understand “analyticity” of the family are clarified. This is then applied to obtain some general results on the stability
of the analyticity of the family under perturbations of the generators. 相似文献
2.
3.
S. Kantorovitz 《Semigroup Forum》2001,62(3):473-476
No Abstract.
June 2, 1999 相似文献
4.
Shmuel Kantorovitz 《Semigroup Forum》1996,53(1):262-265
A contraction version of Liu's recent analyticity criterion for semigroups is given a very simple proof based on the exponential
formula. 相似文献
5.
6.
Quasi-Affinity in certain Classes of Operators 总被引:1,自引:0,他引:1
The family of operators S + V (, C, Re > 0), where V isan injective S-Volterra operator (that is, [S, V[ = V2) and A V1 generates a uniformly bounded C0-semigroup,is studied in the context of similarity and of the weaker quasi-affinityrelation. It is shown that S is similar to S + V for all , C,Re > 1, and is a quasi-affine transform of S + tV for allt 0 and 0 < < 1. 相似文献
7.
Shmuel Kantorovitz 《Semigroup Forum》2009,78(2):285-292
The “Volterra relation” is the commutation relation [S,V]⊂V
2, where S is a not necessarily bounded operator, V is a bounded operator leaving D(S) invariant, and [⋅,⋅] is the Lie product. When S,V are so related, and in addition iS generates a bounded C
0-group of operators and V has some general property, it is known that S+α
V (α∈ℂ) is similar to S if and only if ℜ
α=0 (cf. Theorem 11.17 in Kantorovitz, Spectral Theory of Banach Space Operators, Springer, Berlin, 1983). In particular, S−V is not similar to S. However, it is shown in this note that (without any restriction on
V
and on the group
S(⋅) generated by
iS), the perturbations (S−V)+P are similar to S for all P in the similarity sub-orbit {S(a)VS(−a);a∈ℝ} of V. When S is bounded, the above perturbations are similar to S for all P in the wider similarity sub-orbit {e
aS
Ve
−aS
;a∈ℂ}. 相似文献
8.
9.
Let be a module finite extension of normal domains. We show that if is unramified in codimension one and if has finite projective dimension over , then is étale over . Our proof makes use of P. Roberts' New Intersection Theorem.
10.
Abstract Volterra Relation 总被引:1,自引:1,他引:0
The abstract Volterra relation is the relation
, satisfied by a closed operator S and a bounded operator V over some complex Banach space X. Results of several articles
of the second author are extended from the case of S bounded to the general case. These include results on similarity, quasi-affinity,
Cn-classification, and growth of
related semigroups. 相似文献