Mean ergodicity of weighted composition operators on spaces of holomorphic functions

[EN] Let phi be a self-map of the unit disc D of the complex plane C and let psi be a holomorphic function on D. We investigate the mean ergodicity and power boundedness of the weighted composition operator C-phi,C-psi(f) = psi(f o phi) with symbol phi and multiplier psi on the space H(D). We obtain necessary and sufficient conditions on the symbol phi and on the multiplier psi which characterize when the weighted composition operator is power bounded and (uniformly) mean ergodic. One necessary condition is that the symbol phi has a fixed point in D. If phi is not a rational rotation, the sufficient conditions are related to the modulus of the multiplier on the fixed point of phi. Some of our results are valid in an open connected set U of the complex plane.This research was partially supported by MINECO, Project MTM2013-43540-P. The second and third authors were partially supported by GVA, Project AICO/2016/054.Beltrán Meneu, MJ.; Gómez Collado, MDC.; Jorda Mora, E.; Jornet Casanova, D. (2016). Mean ergodicity of weighted composition operators on spaces of holomorphic functions. Journal of Mathematical Analysis and Applications. 444(2):1640-1651. https://doi.org/10.1016/j.jmaa.2016.07.039S16401651444

Serum Antibody Response to Polysaccharides in Children with Recurrent Respiratory Tract Infections

We evaluated children (15-months old and older) with recurrent upper respiratory tract infections and normal levels of immunoglobulins in serum for specific polysaccharide immunodeficiency using an enzyme-linked immunosorbent assay method. Results showed that of 12 patients vaccinated with Act-HIB vaccine, one did not develop specific antibodies to Haemophilus influenzae type b, demonstrating that such immunodeficiency is present in Costa Rican children

Genetic, molecular and functional analyses of complement factor I deficiency.

Complete deficiency of complement inhibitor factor I (FI) results in secondary complement deficiency due to uncontrolled spontaneous alternative pathway activation leading to susceptibility to infections. Current genetic examination of two patients with near complete FI deficiency and three patients with no detectable serum FI and also close family members revealed homozygous or compound heterozygous mutations in several domains of FI. These mutations were introduced into recombinant FI and the resulting proteins were purified for functional studies, while transient transfection was used to analyze expression and secretion. The G170V mutation resulted in a protein that was not expressed, whereas the mutations Q232K, C237Y, S250L, I339M and H400L affected secretion. Furthermore, the C237Y and the S250L mutants did not degrade C4b and C3b as efficiently as the WT. The truncated Q336x mutant could be expressed, in vitro, but was not functional because it lacks the serine protease domain. Furthermore, this truncated FI was not detected in serum of the patient. Structural investigations using molecular modeling were performed to predict the potential impact the mutations have on FI structure. This is the first study that investigates, at the functional level, the consequences of molecular defects identified in patients with full FI deficiency