The Applications of Schwartz Distributions
by
O. P. Misra
Department of physics & astrophysics, University of Delhi, Delhi 110007, INDIA

The applicability of functional analysis is known through ``Theorie des Distributions'' created by French mathematician L. Schwartz due to its applications in differential and partial differential equations. However, scientist/applicants have pointed out the deficiencies of the functions in ``Theory of functions'' which occurred in their proposed work. For example, reduction of functions of several variables to unary function (see Schonfinkel [1924]); the deficiencies of functions in the precision of measurement occurred by taking observations in experimental data (see, Hosemann and Bagchi [1962]). The object of the present work is to provide the answer of these problems raised by logician and physicists by making use of `value and limit' at a point of distributions. The operation 'value and limit' of distributions has been discussed earlier by Misra [1986] and also in collaboration with Lavoine (see, Misra and Lavoine [1986]).

References

Hosemann. R., and S.N. Bagchi, Direct Analysis of Diffraction by Matter, North-Holland, Amsterdam, 1962.

Misra, O.P., Some Results of Schwartz Distribution in I^'_{\lambda, \nu} Simon Stevin, Vol.60, No. 3, 1986.

Misra, O.P. and Lavoine, J.L., Transform Analysis of Generalized Functions, North Holland Mathematical Studies, 1986.

Schonfinkel, M., Ueber die Bausteine der mathematischen Logik, Math. Annalen 92, pp.305-316, 1924.

Date received: February 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-33.