Uniform approximation with linear combinations of reproducing kernels

• Autorzy: Jan Mycielski , Stanisław Świerczkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A10: Trigonometric approximation
• 41A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 2
• Strony: 105-114

Daty

wydano

1996

otrzymano

1994-05-10

poprawiono

1996-07-01

Twórcy

autor

Jan Mycielski

• Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395, U.S.A.

autor

Stanisław Świerczkowski

• Department of Mathematics and Computing, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman

Bibliografia

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