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Doctoral Thesis
DOI
Document
Author
Full name
Angelina Carrijo de Oliveira Ganancin Faria
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Jordão, Thaís (President)
Bracciali, Cleonice Fatima
Peron, Ana Paula
Sant'Anna, Douglas Azevedo
Title in Portuguese
Ferramentas de Aproximação em Espaços Compactos 2-Homogêneos
Keywords in Portuguese
Condição de Hölder
Decrescimento de sequências de autovalores
K-funcional
Módulo de suavidade fracionário
Raio de aproximação
Abstract in Portuguese
Neste trabalho apresentamos duas caracterizações para o K-funcional do tipo Peetre sobre os espaços compactos 2-homogêneos. Provamos a equivalência no sentido assintótico entre o módulo de suavidade de ordem fracionária e o K-funcional do tipo Peetre, e a equivalência deste último com o raio de aproximação de um operator multiplicativo definido para este propósito. Como consequência obtivemos a desigualdade de Marchaud, neste contexto. Estes resultados generalizam os equivalentes, e bem conhecidos, sobre o contexto esférico. As caracterizações foram aplicadas para mostrar que uma condição abstrata de Hölder, ou de diferenciabilidade de ordem finita, sobre núcleos que geram operadores integrais positivos, implica a obtenção de uma taxa de decrescimento polinomial para suas sequências de autovalores.
Title in English
Approximation Tools on Compact Two-Point Homogeneous Spaces
Keywords in English
Decay of eigenvalue sequences
Fractional modulus of smoothness
Hölder condition
K-functional
Rate of approximation
Abstract in English
We prove two characterization for the Peetre type K-functional on M, a compact two-point homogeneous space. One in terms the rate of approximation of a family of multipliers operator defined to this purpose, and another in terms of the fractional moduli of smoothness. As a direct consequence of those we obtained the Marchaud inequality on this framework. These extend the well known results on the spherical setting. The characterizations are employed to show that an abstract Hölder condition or finite order of differentiability condition imposed on kernels generating certain operators implies a sharp decay rates for their eigenvalues sequences.
 
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Publishing Date
2019-10-02
 
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