Open AccessFunctional Calculus for the Series of Semigroup Generators Via Transference
Author(s) -
Shawgy Hussein,
Simon Joseph,
Ahmed Sufyan,
Murtada Amin,
Ranya Tahire,
Hala Taha
Publication year - 2019
Publication title -
global journal of science frontier research
Language(s) - English
Resource type - Journals
eISSN - 2249-4626
pISSN - 0975-5896
DOI - 10.34257/gjsfrfvol19is5pg57
Subject(s) - mathematics , semigroup , sequence (biology) , bounded function , generator (circuit theory) , hilbert space , banach space , holomorphic functional calculus , functional calculus , pure mathematics , holomorphic function , sequence space , ideal (ethics) , cancellative semigroup , discrete mathematics , algebra over a field , approximation property , mathematical analysis , power (physics) , philosophy , genetics , physics , epistemology , quantum mechanics , biology
In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved that if be the sequence generates 0- semigroups on a Hilbert space, then for each the sequence of operators has bounded calculus for the closed ideal of bounded holomorphic functions on right half–plane. The bounded of this calculus grows at most logarithmically as. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m∈ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called semigroups, the Hilbert space results actually hold in general Banach spaces.