Almost normed spaces of functions with polynomial asymptotic behaviour
Journal Article
·
· Sbornik. Mathematics
- V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
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.
- OSTI ID:
- 21208298
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 1 Vol. 194; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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