Sampling-type sets and composition operators on bloch-type spaces1 Report as inadecuate




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The purpose of this article is to survey the recent results on sampling-type sets and composition operators on Bloch{type spaces. Most of them were presented by the authors in two conferences held in Bogota 2011, on the occasion of celebrating the 60th anniversary of the Departamento de Matemáticas, Universidad Nacional de Colombia.

Tipo de documento: Artículo - Article

Palabras clave: Composition operators, Bloch space, sampolig sets.





Source: http://www.bdigital.unal.edu.co


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Bol.
Mat.
18(1), 39–54 (2011) 39 Sampling–type sets and composition operators on Bloch-type spaces1 René Erlı́n Castillo2 Departamento de Matemáticas Universidad Nacional de Colombia Julio César Ramos Fernández3 Departamento de Matemáticas, Universidad de Oriente 6101 Cumaná, Estado de Sucre, Venezuela The purpose of this article is to survey the recent results on sampling– type sets and composition operators on Bloch–type spaces.
Most of them were presented by the authors in two conferences held in Bogotá 2011, on the occasion of celebrating the 60th anniversary of the Departamento de Matemáticas, Universidad Nacional de Colombia. Keywords: Composition operators, Bloch space, sampolig sets. El propósito de este arı́tculo es el de divulgar resultados recientes sobre conjuntos tipo muestreo y del operador de composición en espacios de Bloch.
La mayorı́a de estos resultados fueron presentados por los autores en dos conferencias, las cuales tuvieron lugar en Bogotá 2011, en ocasión de la celebración del 60 aniversario del Departamento de Matemáticas de la Universidad Nacional de Colombia. Palabras claves: operador de composición, espacio de Bloch, conjuntos de muestreos. MSC: 30D45, 30F45, 47B33. 1 The authors wish to express their sincere gratitude to the editors for the invitation to publish our work in Boletı́n de Matemáticas. 2 recastillo@unal.edu.co 3 jcramos@udo.edu.ve 40 Castillo and Ramos Fernández, Sampling–type sets and composition 1 Introduction Let D denote the unit disk in the complex plane C and let H(D) be the space of all holomorphic functions on D with the topology of uniform convergence on compact subsets of D.
A function f ∈ H(D) is said to be a Bloch function if 0 f (z) ≤ Kf , 1 − |z|2 (1) for all z ∈ D and for some positive constant Kf depending on f .
The set of all Bloch functions is an F –space which is denoted as B.
The idea of consider this kind of functions is d...






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