Descripción: We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert-Schmidt bounded type, are locally m-convex Fréchet algebras. We prove that the spectrum of these algebras has a natural analytic structure, which we use to characterize the envelope of holomorphy. We also show a Cartan-Thullen type theorem. © 2011 Elsevier Inc.

Descripción: We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect to the algebra of bounded type holomorphic functions, in terms of the spectrum of the algebra. We then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity. We show that for bounded balanced sets, extensions to the envelope are always of bounded type, and that this does not necessarily hold for unbounded sets, answering a question posed by Hirschowitz in 1972. We also consider extensions to open subsets of the bidual, present some Banach-Stone type results and show some properties of the spectrum when the domain is the unit ball of ℓ p. © 2011 Elsevier Inc.

Descripción: A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class. © 2007 Elsevier Inc. All rights reserved.

Descripción: Alternative splicing plays a key role in generating protein diversity. Transfections with minigenes revealed coordination between two distant, alternatively spliced exons in the same gene. Mutations that either inhibit or stimulate inclusion of the upstream alternative exon deeply affect inclusion of the downstream one. However, similar mutations at the downstream alternative exon have little effect on the upstream one. This polar effect is promoter specific and is enhanced by inhibition of transcriptional elongation. Consistently, cells from mutant mice with either constitutive or null inclusion of a fibronectin alternative exon revealed coordination with a second alternative splicing region, located far downstream. Using allele-specific RT-PCR, we demonstrate that this coordination occurs in cis and is also affected by transcriptional elongation rates. Bioinformatics supports the generality of these findings, indicating that 25% of human genes contain multiple alternative splicing regions and identifying several genes with nonrandom distribution of mRNA isoforms at two alternative regions. Copyright ©2005 by Elsevier Inc.