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Associated weights and spaces of holomorphic functions

Klaus Bierstedt, José Bonet, Jari Taskinen (1998)

Studia Mathematica

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset G ⊂ ℂ N which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...

Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma Akanksha, Girja S. Srivastava (2017)

Mathematica Bohemica

The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space X of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...

Completeness in L1(R) of discrete translates.

Joaquim Bruna, Alexander Olevskii, Alexander Ulanovskii (2006)

Revista Matemática Iberoamericana

We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.

Construction of a certain superharmonic majorant

Paul Koosis (1994)

Annales de l'institut Fourier

Given a function f ( t ) ≥ 0 on ℝ with ∫ - ∞ ∞ ( f ( t ) / ( 1 + t 2 ) ) d t < ∞ and | f ( t ) - f ( t ' ) | ≤ l | t - t ' | , a procedure is exhibited for obtaining on ℂ a (finite) superharmonic majorant of the function F ( z ) : 1 π ∫ - ∞ ∞ | 𝔍 z | | z - t | 2 f ( t ) d t - A l | 𝔍 z | , where A is a certain (large) absolute constant. This leads to fairly constructive proofs of the two main multiplier theorems of Beurling and Malliavin. The principal tool used is a version of the following lemma going back almost surely to Beurling: suppose that f ( t ) , positive and bounded away from 0 on ℝ , is such that ∫ - ∞ ∞ ( f ( t ) / ( 1 + t 2 ) d t < ∞ and denote, for any constant α > 0 and each x ∈ ℝ , the unique...

Convergence of Taylor series in Fock spaces

Haiying Li (2014)

Studia Mathematica

It is well known that the Taylor series of every function in the Fock space F α p converges in norm when 1 < p < ∞. It is also known that this is no longer true when p = 1. In this note we consider the case 0 < p < 1 and show that the Taylor series of functions in F α p do not necessarily converge “in norm”.

Deux exemples sur la dimension moyenne d’un espace de courbes de Brody

Bernardo Freitas Paulo da Costa (2013)

Annales de l’institut Fourier

On étudie la dimension moyenne de l’espace de courbes 1 -Brody à valeurs dans deux surfaces complexes  : d’abord pour des surfaces de Hopf, et ensuite pour P 2 privé d’une droite. On montre dans le premier cas que la dimension moyenne est nulle via une borne sur la croissance des fonctions holomorphes faisant apparaître le lemme de la dérivée logarithmique. Pour montrer la positivité dans le deuxième exemple, on relève de la droite à son complémentaire un espace de courbes de Brody de dimension moyenne...

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