Displaying similar documents to “Inverse problems for periodic transport equations”

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

Ka-Sing Lau, Jian-Rong Wang, Cho-Ho Chu (1995)

Studia Mathematica

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The Choquet-Deny theorem and Deny’s theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the L p -dimension, the L p -density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.

Measures connected with Bargmann's representation of the q-commutation relation for q > 1

Ilona Królak (1998)

Banach Center Publications

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Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product 〈 z n , z k 〉 q = δ n , k [ n ] q ! = F ( z n z ¯ k ) . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.