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Sequential approach to integrable distributions. (English) Zbl 1265.46056

The test function space for integrable distributions is the space \(\mathcal B_0\) of smooth functions vanishing at infinity together with all of their derivatives. The list of equivalent conditions for a distribution to be integrable is given in [P. Dierolf and J. Voigt, Collect. Math. 29, 185–195 (1978; Zbl 0393.46034)]. By the use of the notion of unit-sequences and special-unit sequences, the author extends distributions from \(\mathcal B_0\) to its bidual space in the appropriate topology of smooth functions. This construction leads to an extension of the list of various equivalent conditions for integrability of distributions.

MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions

Citations:

Zbl 0393.46034
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