Distribution semigroups on \(\mathcal K_1\). (English) Zbl 1110.47304

Mijatović, M.; Pilipović, S.

Bull., Cl. Sci. Math. Nat., Sci. Math. 127, No. 28, 7-16 (2003).

Quasi-distributional and exponentially bounded semigroups of operators were introduced by W.–S.Wang [J. Funct.Anal.146, No.2, 352–381 (1997; Zbl 0902.47032)] and P.C.Kunstmann [Trans.Am.Math.Soc.351, No.2, 837–856 (1999; Zbl 0983.47028)]. The authors change the basic space into the test-function space for exponentially bounded distributions \(\mathcal K_1\). After that, they analyze an infinitesimal generator of a semigroup belonging to one of the above mentioned operator semigroups. The obtained results correspond to the ones from the papers cited above.

Reviewer: Marko Nedeljkov (Novi Sad)

MSC:

47D06	One-parameter semigroups and linear evolution equations
46F10	Operations with distributions and generalized functions

Keywords:

distribution semigroups; quasi-distribution semigroups; integrated semigroups

Citations:

Zbl 0902.47032; Zbl 0983.47028