Jose Maria Almira

Learn More
We prove that, if (C[a, b], {A n }) is an approximation scheme and (A n) satisfies de La Vallée-Poussin Theorem, there are instances of continuous functions on [a, b], real analytic on (a, b], which are " poorly approximable " by the elements of {A n }. This illustrates the thesis that the smoothness conditions guaranteeing that a function is " well(More)
We prove the existence of a dense subset ∆ of [0,4] such that for all α ∈ ∆ there exists a subgroup X α of infinite rank of Z[z] such that X α is a discrete subgroup of C[0,β] for all β ≥ α but it is not a discrete subgroup of C[0,β] for any β ∈ (0,α). Given a set of nonnegative real numbers Λ = {λ i } ∞ i=0 , a Λ-polynomial (or Müntz polynomial) is a(More)
The main goal of this paper is to study some elementary properties of polynomial and rational approximation in the setting of approximation spaces of analytic functions defined on compact subsets of the complex plane. Concretely, we are interested in convergence of Faber series and existence of best rational approximation in the norm of these spaces. For(More)
In this note we give a new proof of Hilbert's Nullstellensatz, based on the use of Gröbner basis. The proof has two variants. The first one uses the fundamental theorem of algebra and the second one uses Gelfand-Mazur's theorem.
  • 1