Nearstandard operators

Author
T. Kudryk, V. Lyantse, G. Ghuiko
Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Abstract
In the paper [1] by means of stadard filling notion a structure of nearstandardness has been introduced on the set ${\Bbb T}$ finite in the sense of E. Nelson's IST [4,5]. Now we extend this structure on linear operators acting in the space ${\Bbb C}^{\Bbb T}$. The examples related to the discrete differentiation, discrete analogues of the Fourier-transform and the Riemann-Lebesgue are studied.
Keywords
nearstandardness, standard filling, E. Nelson's IST, finite set, linear operators, discrete differentiation
DOI
doi:10.30970/ms.3.1.29-40
Reference
1. Kudryk T., Lyantse V. and Chuiko G. Nearstandardness on finite set// Matematychni Studii, V.2. 1993. - P. 25–34.

2. Albeverio S., Fenstad J., Hoegh-Krohn T., Lindstrom T. Nonstandard methods in stochastic analysis and mathematical physics. – New York: Academic Press, 1986.

3. Davis M. Applied nonstandard analysis. A Wiley - Interscience publication. John Wiley & Sons. New Jork–London–Sydney–Toronto, 1977.

4. Nelson E. Internal set theory: a new approach to nonstandard analysis // Bull. Amer. Math. Soc. 1977. V.83, N.6. P.1165–1198.

5. Nelson E. Radically elementary probability theory. – Princeton, New Jersey: Princeton University Press, 1987. 97 p. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine

Pages
29-40
Volume
3
Issue
1
Year
1994
Journal
Matematychni Studii
Full text of paper
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