Resolvent characterisation of generators of cosine functions and C0-groups

被引:4
|
作者
Krol, Sebastian [1 ]
机构
[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland
关键词
Cosine function; C-0-group; Fattorini's theorem; Functional calculus; Gearhart's theorem; NUMERICAL RANGE; DIFFERENTIAL-EQUATIONS; PERTURBATION THEOREM; LAPLACE TRANSFORM; OPERATORS; CALCULUS; SEMIGROUPS; INVERSION;
D O I
10.1007/s00028-013-0178-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The paper provides new characterisations of generators of cosine functions and C (0)-groups on UMD spaces and their applications to some classical problems in cosine function theory. In particular, we show that on UMD spaces, generators of cosine functions and C (0)-groups can be characterised by means of a complex inversion formula. This allows us to provide a strikingly elementary proof of Fattorini's result on square root reduction for cosine function generators on UMD spaces. Moreover, we give a cosine function analogue of McIntosh's characterisation of the boundedness of the H (a) functional calculus for sectorial operators in terms of square function estimates. Another result says that the class of cosine function generators on a Hilbert space is exactly the class of operators which possess a dilation to a multiplication operator on a vector-valued L (2) space. Finally, we prove a cosine function analogue of the Gomilko-Feng-Shi characterisation of C (0)-semigroup generators and apply it to answer in the affirmative a question by Fattorini on the growth bounds of perturbed cosine functions on Hilbert spaces.
引用
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页码:281 / 309
页数:29
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