Growth rates for sums of i.i.d. Hilbert space valued random variables

1981 ◽  
pp. 153-175 ◽  
Author(s):  
Victor Goodman
Keyword(s):  
Hilbert Space ◽  
Growth Rates ◽  
Random Variables

scholarly journals Positive Semigroups Using Resolvent Estimate Bounds on Sharp Growth Rates

2020 ◽  
Vol 4 (2) ◽  
pp. p1
Author(s):  
Simon Joseph ◽  
Musa Siddig ◽  
Hafiz Ahmed ◽  
Malik Hassan ◽  
Budur Yagoob
Keyword(s):  
Growth Rate ◽  
Hilbert Space ◽  
Growth Rates ◽  
Continuous Functions ◽  
Resolvent Estimate ◽  
Space Of Continuous Functions ◽  
Strongly Continuous Semigroups ◽  
Positive Semigroups ◽  
Underlying Space ◽  
Sharp Growth

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.

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