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This article is cited in 6 scientific papers (total in 7 papers)
Almost normed spaces of functions with polynomial asymptotic behaviour
L. D. Kudryavtsev Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We consider a linear space of functions asymptotically approaching
polynomials of degree not higher than a fixed one as the independent
variable approaches infinity. Such a space cannot be normed
if the functions in it possess a certain smoothness. For this reason the concept
of almost normed space is introduced and the spaces in question,
namely, spaces of functions asymptotically or strongly asymptotically
approaching polynomials, are shown to be almost normed.
The completeness of these spaces in the metric generated
by their almost norm is also proved, the connection between
the asymptotic approach and the strong asymptotic approach of functions to polynomials
is studied, and a new (and shorter) proof of the criterion for the asymptotic
approach of functions to polynomials is presented.
Received: 17.04.2002
Citation:
L. D. Kudryavtsev, “Almost normed spaces of functions with polynomial asymptotic behaviour”, Mat. Sb., 194:1 (2003), 103–120; Sb. Math., 194:1 (2003), 105–122
Linking options:
https://www.mathnet.ru/eng/sm708https://doi.org/10.1070/SM2003v194n01ABEH000708 https://www.mathnet.ru/eng/sm/v194/i1/p103
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Abstract page: | 460 | Russian version PDF: | 181 | English version PDF: | 15 | References: | 52 | First page: | 2 |
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