Uniform approximation with linear combinations of reproducing kernels

Jan Mycielski; Stanisław Świerczkowski

Studia Mathematica (1996)

  • Volume: 121, Issue: 2, page 105-114
  • ISSN: 0039-3223

Abstract

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We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.

How to cite

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Mycielski, Jan, and Świerczkowski, Stanisław. "Uniform approximation with linear combinations of reproducing kernels." Studia Mathematica 121.2 (1996): 105-114. <http://eudml.org/doc/216345>.

@article{Mycielski1996,
abstract = {We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.},
author = {Mycielski, Jan, Świerczkowski, Stanisław},
journal = {Studia Mathematica},
language = {eng},
number = {2},
pages = {105-114},
title = {Uniform approximation with linear combinations of reproducing kernels},
url = {http://eudml.org/doc/216345},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Mycielski, Jan
AU - Świerczkowski, Stanisław
TI - Uniform approximation with linear combinations of reproducing kernels
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 2
SP - 105
EP - 114
AB - We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.
LA - eng
UR - http://eudml.org/doc/216345
ER -

References

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  1. [1] L. de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, N.J., 1968. Zbl0157.43301
  2. [2] Y. Cenzer, Row-action methods for huge and sparse systems and their applications, SIAM Rev. 23 (1981), 444-466. Zbl0469.65037
  3. [3] V. Faber and J. Mycielski, Applications of learning theorems, Fund. Inform. 15 (1991), 145-167. Zbl0764.68142
  4. [4] G. B. Folland, Harmonic Analysis in Phase Space, Princeton Univ. Press, 1989. Zbl0682.43001
  5. [5] S. Kaczmarz, Angenäherte Auflösung von Systemen linearer Gleichungen, Bull. Acad. Polon. Sci. Lett. A 35 (1937), 355-357. Zbl0017.31703
  6. [6] J. Mycielski, Can mathematics explain natural intelligence?, Phys. D 22 (1986), 366-375. Zbl0611.92031
  7. [7] J. Mycielski, A learning theorem for linear operators, Proc. Amer. Math. Soc. 103 (1988), 547-550. Zbl0653.41021
  8. [8] J. Mycielski and S. Świerczkowski, A model of the neocortex, Adv. Appl. Math. 9 (1988), 465-480. Zbl0662.68087
  9. [9] W. Rudin, Functional Analysis, McGraw-Hill, 1973. 
  10. [10] S. Saitoh, Theory of Reproducing Kernels and its Applications, Longman Sci. & Tech., Harlow, and Wiley, New York, 1988. Zbl0652.30003
  11. [11] J. Stewart, Positive definite functions and generalizations, an historical survey, Rocky Mountain J. Math. 6 (1976), 406-434. Zbl0337.42017
  12. [12] N. Wiener, The Fourier Integral and Certain of its Applications, Cambridge Univ. Press, 1967, 1933. Zbl0006.05401
  13. [13] K. Yosida, Functional Analysis, 5th ed., Springer, Berlin, 1980. 

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