Order equalities for some functionals and their application to the estimation of the best <Emphasis Type="Italic">n</Emphasis>-term approximations and widths |
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| Authors: | A L Shydlich |
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| Institution: | (1) Department of Geological and Atmospheric Sciences, Iowa State University, 3021 Agronomy Building, Ames, IA, USA;(2) Department of Meteorology, Federal University of Technology, Akure, Nigeria;(3) Teraflux Corporation, Boca Raton, FL, USA; |
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| Abstract: | We study the behavior of functionals of the form
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$ \mathop {\sup }\limits_{l > n} \left( {l - n} \right){\left( {\sum\limits_{k = 1}^l {\frac{1}{{{\psi^r}(k)}}} } \right)^{{{ - 1} \mathord{\left/{\vphantom {{ - 1} r}} \right.} r}}}, $ \mathop {\sup }\limits_{l > n} \left( {l - n} \right){\left( {\sum\limits_{k = 1}^l {\frac{1}{{{\psi^r}(k)}}} } \right)^{{{ - 1} \mathord{\left/{\vphantom {{ - 1} r}} \right.} r}}}, |
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