Infinite Differentiability of Hermitian and Positive $C$-Semigroups and $C$-Cosine Functions | Zendy

Yuan-Chuan Li | Zendy; Sen-Yen M. Shaw | Zendy

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Infinite Differentiability of Hermitian and Positive $C$-Semigroups and $C$-Cosine Functions

Author(s) -

Yuan-Chuan Li,

Sen-Yen M. Shaw

Publication year - 1998

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195144424

Subject(s) - mathematics , hermitian matrix , differentiable function , trigonometric functions , pure mathematics , mathematical analysis , geometry

Let C be a bounded linear operator which is not necessarily injective. The following statements are proved: (1) hermitian C-semigroups are infinitely differentiable in operator norm on (0, oo ); (2) hermitian C-cosine functions are norm continuous at either non or all of points in [0, oo ); (3) positive C-semigroups which dominate C are infinitely differentiable in opetator norm on [0, oo ); (4) positive C-cosine functions are infinitely differentiable in operator norm on [0, oo). §

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