Uniform Boundedness of Toeplitz Matrices with Variable Coefficients |
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Authors: | Albrecht Böttcher Sergei Grudsky |
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Affiliation: | 1. Fakult?t für Mathematik, TU Chemnitz, D-09107, Chemnitz, Germany 2. Departamento de Matemáticas, CINVESTAV del I.P.N, Apartado Postal 14-740, 07000, México, D.F., México
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Abstract: | Uniform boundedness of sequences of variable-coefficient Toeplitz matrices is a delicate problem. Recently we showed that if the generating function of the sequence belongs to a smoothness scale of the H?lder type and if α is the smoothness parameter, then the sequence may be unbounded for α < 1/2 while it is always bounded for α > 1. In this paper we prove boundedness for all α > 1/2. This work was partially supported by CONACYT project U46936-F, Mexico. |
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Keywords: | Primary 47B35 Secondary 15A60, 65F35 |
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