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Positivity

, Volume 14, Issue 4, pp 623–636 | Cite as

Positive almost periodic solutions of some convolution equations

  • Silvia-Otilia Corduneanu
Article
  • 62 Downloads

Abstract

Consider a Hausdorff σ-compact, locally compact abelian group G. We are looking for positive almost periodic solutions of the following functional equation:
$${\displaystyle f(x)=M_y\left[(A\circ f)(xy^{-1})\mu(y)\right], \quad x\in G.}$$
In this context μ is a positive almost periodic measure on G, A is a uniformly continuous function on \({{\mathbb R}}\) and M y [μ(y)] is the mean of μ. A more general equation which we investigate is the following
$${\displaystyle f(x)=g(x)+\nu*f(x)+M_y\left[(A\circ f)(xy^{-1})\mu(y)\right], \quad x\in G,}$$
where g is a positive almost periodic function on Gμ a positive almost periodic measure, ν a positive bounded measure and A a Lipschitz function.

Keywords

Convolution equation Positive solution Almost periodic function Almost periodic measure 

Mathematics Subject Classification (2000)

39B22 42A82 42A85 43A05 43A60 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Mathematics“Gh. Asachi” Technical University of IaşiIasiRomania

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