Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T00:04:41.515Z Has data issue: false hasContentIssue false
  • English
  • Français

On differential polynomials I

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Hisasi Morikawa*
Affiliation:
The University of Aizu, Tsuruga, Ikki-machi, Aizu-Wakamatsu City, Fukushima, 965, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The content of Part I is nothing else than, the theory of binomial polynomial sequences in infinite variables (u(1), u(2), u(3), …) with weight u(1) = l. However, sometimes we are concerned with specialization therefore, we call the elements in K[u(1), u(2), u(3), …] differential polynomials. As analogies of special polynomials with binomial property, we may construct special differential polynomials with binomial property.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 148 , December 1997 , pp. 39 - 72
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[1] Morikawa, H., Some analytic and geometric applications of the invariant theoretic method, Nagoya Math. J., 80 (1980), 1–47.CrossRefGoogle Scholar
[2] Mullin, R. and Rota, G. C., On the foundation of combinatorial theory III—Theory of binomial enumerations, in Graph Theory and it’s Application, Academic Press, New York (1970).Google Scholar
[3] Roman, S. and Rota, G. C., The umbral calculus, Adv. in Math., 27 (1978), 95–185.CrossRefGoogle Scholar
[4] Rota, G. C., Finite Operator Calculus, Academic Press, New York, 1975.Google Scholar
[5] Rota, G. C., Kahaner, D. and Odlyzko, A., On the foundations of combinatorial theory VIII—Finite operator calculus, J. Math. Anal. Appl., 42 (1993), 684–760.CrossRefGoogle Scholar