Relatório de pesquisa 01/08
Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces, A. Kushpel and S. Tozoni, submitted January 2008.
Abstract
Using multiplier operators we introduce a thin scale of function
spaces on symmetric two-point homogeneous manifolds. Different spaces
of smooth functions including sets of finite, infinite and analytic
smoothness are considered. Sharp in sense of order estimates of
respective entropy numbers and $n$-widths are established for a general
class of multiplier operators. Various applications of these results
are considered for different multiplier operators. In particular, sharp
order estimates of entropy and widths of Sobolev's classes are found. A
range of sharp order estimates for entropy and widths is
established for sets of finitely and infinitely smooth and analytic
functions on two-point homogeneous manifolds. The results we derive are
apparently new even in the one dimensional case.
Mathematics Subject Classifications
(2000):
Keywords:
If you are interested in obtaining a copy of this Report please contact
the author(s) either via e-mail or by snail mail, at the
address:
IMECC, UNICAMP
Cx. P. 6065
13083-970 Campinas, SP, BRAZIL
January 16, 2008
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