This work is an introduction to anisotropic spaces of holomorphic functions, which have -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding space. We establish a description of via the Bloch classes for all .
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.
We are interested on families of formal power series in parameterized by (). If every is a polynomial whose degree is bounded by a linear function ( for some and ) then the family is either convergent or the series for all except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...