Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
| Autor: | Óscar Ciaurri, Jose L. Ansorena, Juan L. Varona, Fernando Albiac |
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| Přispěvatelé: | Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Work (thermodynamics) Basis (linear algebra) Unconditional basis General Mathematics 010102 general mathematics 01 natural sciences symbols.namesake L-p-spaces Jacobi polynomials symbols Thresholding greedy algorithm Quasi-greedy basis 0101 mathematics Classical theorem Fourier series Mathematics |
| Zdroj: | Academica-e: Repositorio Institucional de la Universidad Pública de Navarra Universidad Pública de Navarra Academica-e. Repositorio Institucional de la Universidad Pública de Navarra instname |
| Popis: | We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we show that no normalized unconditional basis in L-p, p not equal 2, can be semi-normalized in L-q for q not equal p, thus extending a classical theorem of Kadets and Pelczynski from 1968. The first two authors were partially supported by the Spanish Research Grant Analisis Vectorial, Multilineal y Aplicaciones, reference number MTM2014-53009-P, and the last two authors were partially supported by the Spanish Research Grant Ortogonalidad, Teoria de la Aproximacion y Aplicaciones en Fisica Matematica, reference number MTM2015-65888-C4-4-P. The first-named author also acknowledges the support of Spanish Research Grant Operators, lattices, and structure of Banach spaces, with reference MTM2016-76808-P. |
| Databáze: | OpenAIRE |
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