Rate of convergence of Thresholding Greedy Algorithms

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Abstract

The rate of convergence of the classical Thresholding Greedy Algorithm with respect to some bases is studied. We bound the error of approximation by the product of two norms, the norm of f">f and the A1">A1-norm of f">f. We obtain some results for greedy bases, unconditional bases and quasi-greedy bases. In particular, we prove that our bounds for the trigonometric basis and Haar basis are optimal.

About the authors

Vladimir Nikolaevich Temlyakov

Steklov Mathematical Institute of Russian Academy of Sciences; Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics; University of South Carolina

Author for correspondence.
Email: temlyak@math.sc.edu
Doctor of physico-mathematical sciences, Professor

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