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C-Cosine Functions and the Abstract Cauchy Problem, I

✍ Scribed by Chung-Cheng Kuo; Sen-Yen Shaw

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
225 KB
Volume
210
Category
Article
ISSN
0022-247X

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✦ Synopsis

If A is the generator of an exponentially bounded C-cosine function on a Ε½ . Banach space X, then the abstract Cauchy problem ACP for A has a unique Ε½ . Ε½ . y 1 Ε½ . solution for every pair x, y of initial values from y A C X . The main result is a characterization of the generator of a C-cosine function, which may not be exponentially bounded and may have a nondensely defined generator, in terms of the associated ACP.

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