Tsukuba Journal of Mathematics

Generalized number system and its applications (I)

Shutang Wang

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Abstract

This is a further study of the work published in [2]. A generalized number system is established. The generalized functions denote the functions with generalized number system as their domain and range spaces which are different essentially from the Schwartz distributions. For such functions we define $(GNL)$ and $(G)$ integrals which can be considered as the generalization of the Lebesgue integral for real functions. Dirac $\delta$ function can be naturally represented by our generalized functions. This representation is more straightforward than the Schwartz distribution theory. Moreover, each distribution can be described by a generalized function in a natural way.

Article information

Source
Tsukuba J. Math., Volume 9, Number 2 (1985), 203-215.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496160284

Digital Object Identifier
doi:10.21099/tkbjm/1496160284

Mathematical Reviews number (MathSciNet)
MR818204

Citation

Wang, Shutang. Generalized number system and its applications (I). Tsukuba J. Math. 9 (1985), no. 2, 203--215. doi:10.21099/tkbjm/1496160284. https://projecteuclid.org/euclid.tkbjm/1496160284


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