A Generalized Fatou Theorem

A Fatou Type Theorem for Complex Map Germs

In this paper we prove a Fatou type theorem for complex map germs. More precisely, we give (generic) conditions assuring the existence of parabolic curves for complex map germs tangent to the identity, in terms of existence of suitable formal separatrices. Such a map cannot have finite orbits.

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

A Fatou Theorem for the General One- Dimensional Parabolic Equation

(1.1) du/dt = 9u = a{x)uxx + b{x)ux + c{x)u in R x (0, T) where T ^ oo. Here a(x) ^ 0, c(x) S M, l/«(x), b(x)/a(x) and c(x)/a(x) are locally integrable in R, but otherwise the coefficients are unrestricted. The results below extend characterizations of Widder ([17], [18]) for positive solutions of the heat equation (see §1.1). In particular, we find that all positive solutions of (1.1) are of t...

A Fixed Point Theorem in Generalized D-metric Spaces

A General Fatou Lemma

A general Fatou Lemma is established for a sequence of Gelfand integrable functions from a vector Loeb space to the dual of a separable Banach space or, with a weaker assumption on the sequence, a Banach lattice. A corollary sharpens previous results in the …nite dimensional setting even for the case of scalar measures. Counterexamples are presented to show that the results obtained here are sh...