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Estimates of approximation numbers and applications |
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| Authors: | Veli Shakhmurov |
| Affiliation: | 1. Department of Electronics Engineering and Communication, Okan University, Akfirat, Tuzla, 34959, Istanbul, Turkey |
| Abstract: | In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained. |
| Keywords: | Approximation numbers Kolmogorov numbers separable boundary value problems differential-operator equations Banach-valued function spaces operator-vMued multipliers interpo- lation of Banach spaces |
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