Nearstandard operators |
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| Author |
Department of Mechanics and Mathematics, Lviv University, Universytetska 1,
Lviv, 290602, Ukraine
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| 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.
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| Keywords |
nearstandardness, standard filling, E. Nelson's IST, finite set, linear operators, discrete differentiation
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| DOI |
doi:10.30970/ms.3.1.29-40
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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
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| Volume |
3
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| Issue |
1
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| Year |
1994
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| Journal |
Matematychni Studii
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| Full text of paper | |
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