Open AccessPositive Semigroups Using Resolvent Estimate Bounds on Sharp Growth Rates
Author(s) -
Simon Joseph,
Musa Siddig,
H Soliman Ahmed.,
Malik Hassan,
Budur Yagoob
Publication year - 2020
Publication title -
applied science and innovative research
Language(s) - English
Resource type - Journals
eISSN - 2474-4980
pISSN - 2474-4972
DOI - 10.22158/asir.v4n2p1
Subject(s) - resolvent , mathematics , semigroup , hilbert space , banach space , space (punctuation) , sequence space , mathematical analysis , resolvent formalism , sequence (biology) , pure mathematics , finite rank operator , philosophy , linguistics , biology , genetics
In this paper, we study growth rates for strongly continuous semigroups. We fixate that a growth rate for the resolvent estimate on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the semigroup is asymptotically analytic, or if the semigroupis positive and the underlying space is an -space or a space of continuous functions. Also proved variations of the main results on fractional domains; these are valid on more general Banach spaces by Jan Rozendaal and Mark Veraar. In the second part apply the main theorem to prove optimality in a classical example of a perturbed wave equation which shows unusual sequence of spectral behavior.