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Optimal and Non-optimal Rates of Approximation for Integrated Semigroups and Cosine Functions

โœ Scribed by Jung-Chan Chang; Sen-Yen Shaw

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
332 KB
Volume
90
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

For a general approximation process we formulate theorems concerning rates of convergence, including theorems about saturation class, non-optimal rates, and sharpness of non-optimal convergence. The general results are then applied to n-times integrated semigroups and cosine functions, yielding some new results about their approximation, as well as the convergence of their Cesa ro and Abel means to the identity. 1997 Academic Press &S \ x&x&=b (,( )) ( \ ร„ ) is an invariant element of [S \ ], i.e., S \ x=x for all \ # (0, ), and if the set F[X; S \ ]=[x # X; &S \ x&x&=O(,( ))( \ ร„ )] article no. AT963085 200

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