The quantization for in-homogeneous self-similar measures with in-homogeneous open set condition

摘要

Let (g(i))(i=1)(M) be a family of contractive similitudes satisfying the open set condition. Let nu be a self-similar measure associated with (g(i))(i=1)(M) . We study the quantization problem for the in-homogeneous self-similar measure mu associated with a condensation system ((f(i))(i=1)(N), (p(i))(i=0)(N) ,nu). Assuming a version of in-homogeneous open set condition for this system, we prove the existence of the quantization dimension for mu of order r is an element of (0,infinity) and determine its exact value xi(r). The finiteness and positivity of the xi(r)-dimensional upper and lower quantization coefficient are also explored.