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Demi-linear analysis. II: Demi-distributions. (English) Zbl 1488.46073

Summary: In this paper, we develop the theory of demi-distributions which generalizes the usual distribution theory. In particular, we show that many results on differentiations, Fourier transforms, and convolutions can be generalized to demi-distributions theory.
For Part I, see [R. Li et al., J. Korean Math. Soc. 46, No. 3, 643–656 (2009; Zbl 1200.46005)].

MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions
46F10 Operations with distributions and generalized functions

Citations:

Zbl 1200.46005
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References:

[1] Li, R.; Zhong, S.; Li, L., Demi-linear analysis I—basic principles, J Korean Math Soc, 46, 3, 643-656 (2009) · Zbl 1200.46005 · doi:10.4134/JKMS.2009.46.3.643
[2] Li, R.; Zhong, S.; Cui, C., New basic principles of functional analysis (Abstract), J Yanbian Univ, 30, 3, 157-160 (2004)
[3] Wilansky, A., Modern Methods in Topological Vector Spaces (1978), New York: McGraw-Hill, New York · Zbl 0395.46001
[4] Gelfand, I. M., Generalized Functions II (1968), New York: Academic Press, New York · Zbl 0159.18301
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