Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T17:23:58.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrange's theorem for weak functions of several variables

Part of:Distributions, generalized functions, distribution spaces

Published online by Cambridge University Press:  26 February 2010

M. D. Quinn
M. D. Quinn
Affiliation:
Department of Mathematics, The University of Dundee.
Get access

Summary

This paper contains a derivation of Lagrange's expansion with remainder for a weak function of several independent variables each satisfying an implicit relation. We also provide necessary and sufficient conditions for the associated infinite series expansion.

MSC classification

Secondary:46F10: Operations with distributions

Information

Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978, pp. 160 - 178
Copyright
Copyright © University College London 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Chaundy, T.. The differential calculus (Oxford University Press, 1935).Google Scholar
2.Good., I. J. “Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes”, Proc. Cam. Phil. Soc, 56 (1960), 367–380.CrossRefGoogle Scholar
3.Goursat, E.. Cours d'analyse mathématique, 5th ed., Vols. I and II (Gauthier-Villars, 1927 and 1929).Google Scholar
4.Jones., D. S. “Lagrange's Theorem for weak functions”, Mathematika, 13 (1966), 158–171.CrossRefGoogle Scholar
5.Jones., D. S.Generalised functions (McGraw-Hill, 1966).Google Scholar
6.Mirsky, L.. An introduction to linear algebra (Oxford, 1955).Google Scholar
7.Sack., R. A. “Interpretation of Lagrange's expansion and its generalizations to several variables as integration formulas”, J. SIAM. Appl. Math., 13 (1965), 47–59.CrossRefGoogle Scholar
8.Whittaker, E. T. and Watson., G. N.Modern analysis (Cambridge University Press, 1927).Google Scholar