FUNCTIONAL CALCULUS IN THE ALGEBRA OF GENERALIZED HYPERFUNCTIONS ON THE CIRCLE AND APPLICATIONS
Résumé
This paper deals with a functional calculus in the algebra HpTq of generalized hyperfunctions on the circle. This is done introducing an inductive family of complete ultrametric sub-algebras. Power series expansions of classical functions such as the exponential, logarithm or power ones are considered. As an application , a nonlinear Cauchy problem involving fractional powers of generalized hyperfunctions is studied. 1
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