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A Remark on Talenti's Semigroup

Published online by Cambridge University Press:  20 November 2018

Thomas I. Seidman
Thomas I. Seidman*
Affiliation:
University of Maryland, BaltimoreCounty 5401 Wilkens Avenue Baltimore, Maryland 21228, U.S.A.
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For α>0 the Riemann-Liouville Integral J(α) is given for suitable functions g by

1

For a variety of function spaces (e.g., C[0, 1] or Lp(0, 1) with p≥1) this defines a C0 semigroup which has been extensively studied (cf., e.g., [3]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 591 - 592
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Chrysovergis, A., Some Remarks on TalentVs Semigroup, Canad. Math. Bull. 14 (1971), pp. 147–150.Google Scholar
2. Hille, E., review of [1] in Math. Rev., 46 (1973), rev. 9247.Google Scholar
3. Hille, E. and Phillips, R. S., Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ., v. 31.Google Scholar
4. Talenti, G., Sul Problema di Cauchy per le Equazioni a Derivate Parziali, Ann. Mat. Pura Appl., LXVII (1965), pp. 365–394.Google Scholar