Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators

Ghiloni, Riccardo; Recupero, Vincenzo

doi:10.1090/tran/6399

Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
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by Riccardo Ghiloni and Vincenzo Recupero PDF

Trans. Amer. Math. Soc. 368 (2016), 2645-2678 Request permission

Abstract:

The aim of this paper is twofold. On one hand, generalizing some recent results obtained in the quaternionic setting, but using simpler techniques, we prove the generation theorems for semigroups in Banach spaces whose set of scalars belongs to the class of real alternative *-algebras, which includes, besides real and complex numbers, quaternions, octonions and Clifford algebras. On the other hand, in this new general framework, we introduce the notion of spherical sectorial operator and we prove that a spherical sectorial operator generates a semigroup that can be represented by a Cauchy integral formula. It follows that such a semigroup is analytic in time.

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