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Some topological properties of the algebra of generalized hyperfunctions on the circle. (English) Zbl 1013.46031

The author introduces an invariant ultrametric distance in the differential algebra \(H(T)\) of generalized hyperfunctions on the unit circle \(T\). For the induced topology he shows that addition and multiplication are continuous maps. It is also shown that the inversion is a continuous endomorphism of the group of invertible elements of \(H(T)\). Several additional properties of \(H(T)\) are established.

MSC:

46F15 Hyperfunctions, analytic functionals
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