Compactness in approximation spaces

M. Fugarolas

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 2, page 253-262
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Fugarolas, M.. "Compactness in approximation spaces." Colloquium Mathematicae 67.2 (1994): 253-262. <http://eudml.org/doc/210278>.

@article{Fugarolas1994,
abstract = {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.},
author = {Fugarolas, M.},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {253-262},
title = {Compactness in approximation spaces},
url = {http://eudml.org/doc/210278},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Fugarolas, M.
TI - Compactness in approximation spaces
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 2
SP - 253
EP - 262
AB - 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.
LA - eng
UR - http://eudml.org/doc/210278
ER -

References

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  1. [1] Z. Ciesielski, Constructive function theory and spline systems, Studia Math. 53 (1975), 277-302. Zbl0273.41010
  2. [2] A. Pietsch, Approximation spaces, J. Approx. Theory 32 (1981), 115-134. 
  3. [3] S. Ropela, Spline bases in Besov spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 319-325. Zbl0328.41008
  4. [4] B. Simon, Trace Ideals and Their Applications, London Math. Soc. Lecture Note Ser. 35, Cambridge Univ. Press, Cambridge, 1979. 
  5. [5] I. Singer, Bases in Banach Spaces I, Springer, Berlin, 1970. 

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