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Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier, Quentin Menet, Augustin Mouze (2014)

Annales de l’institut Fourier

We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace...

Coarse quantization for random interleaved sampling of bandlimited signals

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Zwith offsets { T n } n = 1 N [ 0 , T ] T n n = 1 N ⊂ [ 0 ,T ] . If the offsetsTn are chosen independently and uniformly at random from  [0,T]  and if the sample values of fare quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error | f ( t ) - f ˜ ( t ) | | f ( t ) − x10ff65;...

Coarse quantization for random interleaved sampling of bandlimited signals∗∗∗

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Z with offsets { T n } n = 1 N [ 0 , T ] . If the offsets Tn are chosen independently and uniformly at random from  [0,T]  and if the sample values of f are quantized with a first order Sigma-Delta algorithm, then with high probability...

Commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1994)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the functions x r e - λ x and x s e + μ x is evaluated for r , s = 0 , 1 , 2 , ... and all λ , μ . Further commutative neutrix convolution products are then deduced.

Compact operators and approximation spaces

Fernando Cobos, Oscar Domínguez, Antón Martínez (2014)

Colloquium Mathematicae

We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.

Compactness in approximation spaces

M. Fugarolas (1994)

Colloquium Mathematicae

In this paper we give a characterization of the relatively compact subsets of the so-called approximation spaces. We treat some applications: (1) we obtain some convergence results in such spaces, and (2) we establish a condition for relative compactness of a set lying in a Besov space.

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