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

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.

MSC:

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