Alexander Gomilko

Bernstein functions and rates in mean ergodic theorems for operator semigroups

We present a functional calculus approach to the study of rates of decay in mean ergodic theorems for bounded strongly continuous operator semigroups. A central role is played by operators of the form g(A, where −A is the generator of the semigroup and g is a Bernstein function. In addition, we obtain some new results on Bernstein functions which are of independent interest.

Product formulas in functional calculi for sectorial operators

We study the product formula

On the Strong Kreiss Resolvent Condition in the Hilbert Space

(fg)(A) = f(A)g(A)

ON RATES IN MEAN ERGODIC THEOREMS

(fg)(A)=f(A)g(A) in the framework of (unbounded) functional calculus of sectorial operators

ON DISCRETE SUBORDINATION OF POWER BOUNDED AND RITT OPERATORS

A

Resolvent representations for functions of sectorial operators

A. We give an abstract result, and, as corollaries, we obtain new product formulas for the holomorphic functional calculus, an extended Stieltjes functional calculus and an extended Hille–Phillips functional calculus. Our results generalise previous work of Hirsch, Martinez and Sanz, and Schilling.