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VIDEO LIBRARY |
Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov
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Spline wavelets and Riemann–Liouville operators in Besov type spaces E. P. Ushakova Steklov Mathematical Institute of Russian Academy of Sciences, Moscow |
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Abstract: With help of spline wavelet systems and corresponding to them decomposition theorems, conditions are found for the fulfillment of inequalities relating the norms of images and pre-images of Riemann–Liouville operators To solve the problem: (1) special systems of spline wavelets of natural orders are constructed; (2) decompositions of elements of the spaces The proofs also use fractional-order spline wavelets developed by T. Blue and M. Unser. Decompositions corresponding to them are used in the work to extract one-sided estimates. As an application of the main results, we study the behavior of sequences of characteristic (approximation and entropy) numbers of Riemann–Liouville operators. From the inequalities for |