Displaying similar documents to “Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures”

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.

Vector valued measures of bounded mean oscillation.

Oscar Blasco (1991)

Publicacions Matemàtiques

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The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained. In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).

Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen (1995)

Studia Mathematica

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We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying ∥ T n ∥ = O ( n β ) as n → ∞ for some β ≥ 0, then ∑ n = 1 ∞ ∥ ( 1 - T ) n x ∥ / ∥ ( 1 - T ) n - 1 x ∥ diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x ≠ 0 .

On the distribution of complex-valued multiplicative functions

Antanas Laurinčikas (1996)

Journal de théorie des nombres de Bordeaux

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Let g j ( m ) , j = 1 , 2 , be complex-valued multiplicative functions. In the paper the necessary and sufficient conditions are indicated for the convergence in some sense of probability measure 1 n card 0 ≤ m ≤ n : ( g 1 ( m ) , g 2 ( m ) ) ∈ A , A ∈ ℬ ( ℂ 2 ) , as n → ∞ .