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- J. M. Almira, A. E. Romero
- 2009

In this paper the characterization as convolution operators of filters sending finite energy signals to bounded signals is used to prove several theoretical results concerning the distance between the ideal filter and the spaces of physically realizable filters. Both the analog and the digital cases are studied and the formulas for the distance and the… (More)

- Jose Maria Almira
- Appl. Math. Lett.
- 2012

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)

- Jose Maria Almira, N. Del Toro, Antonio-Jesús López-Moreno
- Int. J. Math. Mathematical Sciences
- 2005

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)

- J. M. Almira, NULLSTELLENSATZ REVISITED
- 2008

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.

- J. M. Almira
- 2010

In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and n-term approximation for several dictionaries and norms. Moreover, we compare our main theorem with a classical result by… (More)

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