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.

Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators / Ghiloni, Riccardo; Recupero, Vincenzo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 368:4(2016), pp. 2645-2678. [10.1090/tran/6399]

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

Ghiloni, Riccardo;
2016-01-01

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.
2016
4
Ghiloni, Riccardo; Recupero, Vincenzo
Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators / Ghiloni, Riccardo; Recupero, Vincenzo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 368:4(2016), pp. 2645-2678. [10.1090/tran/6399]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/66996
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