caa a22 4500 465825168 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112291 doi (NATIONALLICENCE)springer-10.1007/BF02112291 Some Landau's type inequalities for infinitesimal generators [Elektronische Daten] [H. Kraljević, J. Pečarić] Summary: Lett ↦ T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx ∈D(A 3), the following inequalities hold true: ∥Ax∥3 ⩽ 243/8 ∥x∥2∥A 3 x∥, ∥A 2 x∥ ⩽ 24 ∥x∥∥A 3 x∥2. Ift → T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions. Birkhäuser Verlag, 1990 Kraljević H. Department of Mathematics, University of Zagreb, p.o.b. 187, Y-41001, Zagreb, Yugoslavia aut Pečarić J. Faculty of Technology, University of Zagreb, I.L. Ribara 126, Y-41000, Zagreb, Yugoslavia aut aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 147-153 0001-9054 40:1<147 1990 40 10 https://doi.org/10.1007/BF02112291 text/html Onlinezugriff via DOI 1 book-reviews jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112291 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kraljević H. Department of Mathematics, University of Zagreb, p.o.b. 187, Y-41001, Zagreb, Yugoslavia aut NATIONALLICENCE 700 1- Pečarić J. Faculty of Technology, University of Zagreb, I.L. Ribara 126, Y-41000, Zagreb, Yugoslavia aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 147-153 0001-9054 40:1<147 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer