El Seminario de Matemática Aplicada y Análisis Matemático programa la conferencia ‘On the greedy constant of the Haar system in Lp’ el jueves 13 de noviembre.
José Luis Ansorena Barasoain, profesor Titular de Análisis Matemático de la Universidad de La Rioja, ofrece la charla a las 11.00 horas en el Aula 035 del Complejo Científico-Tecnológico.
Resumen: It is known [6] that the Lp-normalized Haar system is a greedy basis for Lp[0; 1], 1 < p < ?. The proof of this nowadays classical result relies on the characterization of greedy bases as those bases that are simultaneously unconditional and democratic [5]. In this talk we go over some quantitative versions of this characterization, that is, estimates for the greedy constant of a given basis in terms of its unconditionality-type constants and its democracy-type constants, developed throughout several papers [2, 4, 1, 3]. Going furhther, we establish an estimate for the greedy constant of a basis in terms of its suppression unconditionality constant and its bi-democracy constant. Finally, we take advantage of this new estimate for proving that the greedy constant of the Haar system in Lp[0; 1] grows as p* = max {p,p/(p-1)} as p* goes to ?.
Keywords: Haar basis, greedy basis, unconditional basis, democratic basis, Lp spaces, Lebesgue-type inequalities.
Mathematics Subject Classification 2010: 46B15, 41A65.
References:
[1] F. Albiac, and J. L. Ansorena. Characterization of 1-almost greedy bases. Rev. Mat. Complut. 30 (1), 13{24, 2017.
[2] F. Albiac and P. Wojtaszczyk. Characterization of 1-greedy bases. J. Approx. Theory 138 (1), 65-86, 2006.
[3] P. M. Berná, Ó. Blasco, G. Garrigós. Lebesgue inequalities for the greedy algorithm in general bases. Rev. Mat. Complut. 30 (1), 369{392, 2017.
[4] S. J. Dilworth, N. J. Kalton, D. Kutzarova, E. Odell, Th. Schlumprecht and A. Zsák. Renorming spaces with greedy bases. J. Approx. Theory 188, 39{56, 2014.
[5] S. V. Konyagin and V. N. Telmyakov. A remark on greedy approximation in Banach spaces. East J. Approx. 5(3), 365{379, 1999.
[6] V. N. Telmyakov. The best m-term approximation and greedy algorithms. Adv. Comput. Math. 8(3), 249{265, 1998.
El Seminario de Matemática Aplicada y Análisis Matemático está coordinado por Manuel Bello Hernández.
