Estimates for entropy numbers of multipliers operators of Walsh series

• Grant number: 08/07815-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2009
• End date: February 28, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Sergio Antonio Tozoni
• Grantee: Jéssica Milaré
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The Walsh functions form a complete orthonormal system of L^2([0,1]) which has found a lot of applications in many different situations such as, data transmission, filtering, pattern recognition, image enhancement.One of the objectives is the study of some basic results from Martingales Theory such as convergence of martingales and the Doob inequality. Another is the study of L^p-estimates for the square function of martingales and the application of this result in the study of the L^p-convergence of the Walsh series and in the study of a multiplier theorem for Walsh series with the Marcinkiewicz condition.The main objective is to apply the multiplier theorem in the study of the entropy numbers of multipliers operators T of Walsh series and bounded from L^p to L^q, more specifically, the study of the order of decrease of the entropy numbers e_k(T) when k goes to infinity. (AU)