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Product of hyperfunctions on the circle. (English) Zbl 0964.32005
Let \(HF(T)\) be the set of all hyperfunctions on the unit circle \(T\). These objects can be interpreted as natural generalisations of Schwartz distributions on \(T\). The product of two hyperfunctions \(\varphi\in HF(T)\) and \(\psi\in HF(T)\) makes sense if it is possible to compute in some sense the convolution \(\widehat\varphi *\widehat\psi\) and if the sequence \(((\widehat\varphi *\widehat\psi) (n))_{n\in \mathbb{Z}}\) is the sequence of Fourier coefficients of some hyperfunction which the authors call the product of \(\varphi\) and \(\psi\).
Let \(\varphi\) and \(\psi\) be two hyperfunctions on the circle which have disjoint support. Then the authors interpret in terms of Fourier coefficients the fact that their product, defined in the sense of sheaf theory, vanishes.
Reviewer: G.L.N.Rao (Nagpur)

32A45 Hyperfunctions
32C35 Analytic sheaves and cohomology groups
58J15 Relations of PDEs on manifolds with hyperfunctions
46F15 Hyperfunctions, analytic functionals
Full Text: DOI
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