SIX-DIMENSIONAL LANDAU INEQUALITIES

John M. Rassias
1999 Demonstratio Mathematica  
Let X be a complex Banach space, and let t -» T(i)(||T(i)|| < 1, t > 0) be a strongly continuous contraction semigroup (on X) with infinitesimal generator .A.In this paper we prove that the following five inequalities p { X|| 6 < i^iizf-iAir hold for every x G D(A 6 ) and for a fixed number ¿ = 1,2,3,4,5, where iij(6) = j^j [^ such that our symbol [? 1 = • , e6 » . holds as well as ei = 2 1 3 6 5 5 , e 2 = 5 6 7 6 , e 3 = 2 15 , L 1 J l l (6 -1)° 1 £4 = 2 4 3 6 7 6 , e 5 = 2 5 5 5 . Analogous
more » ... 5 5 5 . Analogous inequalities hold for strongly continuous contraction cosine functions. In this case of cosine functions constants iij (6) are replaced by (6) = ((12)!)* [ * ] £i ' I nec l ua^i es are established also for uniformly bounded strongly continuous semigroups and cosine functions. 1991 Mathematics Subject Classification: No. 47D (Algebraic Systems of Linear Operators).
doi:10.1515/dema-1999-0219 fatcat:3s3gsvkw2za7foughlzf2ljikm