Relatório de pesquisa 01/08

Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces, A. Kushpel and S. Tozoni, submitted January 2008.

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): 


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January 16, 2008


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