Positive Semigroups Using Resolvent Estimate Bounds on Sharp Growth Rates

Simon Joseph, Musa Siddig, Hafiz Ahmed, Malik Hassan, Budur Yagoob

Abstract


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.


Full Text:

PDF


DOI: https://doi.org/10.22158/asir.v4n2p1

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Simon Joseph, Musa Siddig, Hafiz Ahmed, Malik Hassan, Budur Yagoob

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © SCHOLINK INC.   ISSN 2474-4972 (Print)    ISSN 2474-4980 (Online)