Pré-duais de espaços de funções holomorfas e dinâmica linear dos operadores de convolução sobre certos espaços de funções inteiras Tese apresentada ao Instituto de Matemática, Estatística e Computação Científica da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obtenção do título de Doutor em Matemática.
A classical result of Godefroy and Shapiro states that every nontrivial convolution operator on the space H(C n ) of entire functions of several complex variables is hypercyclic. In sharp contrast with this result Fávaro and Mujica show that no translation operator on the space H(C N ) of entire functions of infinitely many complex variables is hypercyclic. In this work we study the linear dynamics of convolution operators on H(C N ). First we show that no convolution operator on H(C N ) is neither cyclic nor n-supercyclic for any positive integer n. After we study the notion of Li-Yorke chaos in non-metrizable topological vector spaces and we show that every nontrivial convolution operator on H(C N ) is Li-Yorke chaotic.
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