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Semigroups of Operators and Polynomials of Generators of Bounded Strongly Continuous Groups
Author(s) -
Lei Yansong,
Yi Wanhua,
Zheng Quan
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-69.1.144
Subject(s) - mathematics , semigroup , bounded function , operator (biology) , constructive , differential operator , pure mathematics , bounded operator , discrete mathematics , mathematical analysis , process (computing) , biochemistry , chemistry , repressor , computer science , transcription factor , gene , operating system
Let iA j (l ⩽ j ⩽ n ) be commuting generators of bounded strongly continuous groups, P(A) = Σ |α|⩽m a α A α( A α = A 1 α 1 … A n α n) . By a constructive method, we show that P(A) generates an analytic semigroup, integrated semigroup or C ‐semigroup under different conditions. For P(A) = Σ |α|⩽m a α (t)A α , we also construct the evolution operator or C ‐evolution operator and then show that the initial value problem is well posed. These results can be applied to many differential operators on L P (R n ) (1 ⩽ p < x), C o (R n ) and UC b (R n ).