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Transactions of the American Mathematical Society

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On the division of distributions by analytic functions in locally convex spaces


Author: Denis Chansolme
Journal: Trans. Amer. Math. Soc. 274 (1982), 319-325
MSC: Primary 46F25; Secondary 46G99, 58C10
DOI: https://doi.org/10.1090/S0002-9947-1982-0670935-7
MathSciNet review: 670935
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Abstract: Although the division of distributions by real polynomials and real analytic functions (which are nonzero) is always possible in finite dimensional spaces (from classical results of Hörmander and Lojasiewicz respectively), we show that this is not always possible in infinite dimensional locally convex spaces. In particular, we characterize those locally convex spaces where division is always possible.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0670935-7
Keywords: Infinite dimensional distributions, division by analytic functions
Article copyright: © Copyright 1982 American Mathematical Society

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