Functional calculus estimates for Tadmor–Ritt operators

@article{Schwenninger2016FunctionalCE,
  title={Functional calculus estimates for Tadmor–Ritt operators},
  author={Felix L. Schwenninger},
  journal={Journal of Mathematical Analysis and Applications},
  year={2016},
  volume={439},
  pages={103-124}
}
Abstract We show H ∞ -functional calculus estimates for Tadmor–Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor–Ritt operators in terms of the constant dependence. Furthermore, it is shown how discrete square function estimates influence the functional calculus estimates. 

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References

SHOWING 1-10 OF 63 REFERENCES
On functional calculus properties of Ritt operators
  • F. Lancien, C. L. Merdy
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2015
We compare various functional calculus properties of Ritt operators. We show the existence of a Ritt operator T: X → X on some Banach space X with the following property: T has a boundedExpand
Functional calculus under the Tadmor–Ritt condition, and free interpolation by polynomials of a given degree
For Banach space operators T satisfying the Tadmor–Ritt condition ||(zI−T)−1||⩽C|z−1|−1, |z|>1, we prove that the best-possible constant CT(n) bounding the polynomial calculus for T,Expand
−calculus and Sums of Closed Operators
We develop a very general operator-valued functional calculus for operators with an H ∞ −calculus. We then apply this to the joint functional calculus of two commuting sectorial operators when oneExpand
A note about ritt's condition, related resolvent conditions and power bounded operators
Ritt [17] formulated a condition on the resolvent of a bounded linear operator T, under which he concluded that when n → ∞ In this note we show that Ritt's condition can be related to various otherExpand
Maximal Lp-regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\infty$-functional Calculus
In these lecture notes we report on recent breakthroughs in the functional analytic approach to maximal regularity for parabolic evolution equations, which set off a wave of activity in the lastExpand
The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
Abstract. Given a closed linear operator on a UMD-space, we characterize maximal regularity of the non-homogeneous problem $u' + Au = f$ with periodic boundary conditions in terms of R-boundednessExpand
A Besov class functional calculus for bounded holomorphic semigroups
Abstract It is well-known that π 2 -sectorial operators generally do not admit a bounded H ∞ calculus over the right half-plane. In contrast to this, we prove that the H ∞ calculus is bounded overExpand
The $H^{\infty}-$calculus and sums of closed operators
Abstract. We develop a very general operator-valued functional calculus for operators with an $H^{\infty}-$calculus. We then apply this to the joint functional calculus of two sectorial operatorsExpand
REMARKS ON ℓ1 AND $\ell _{\infty }$-MAXIMAL REGULARITY FOR POWER-BOUNDED OPERATORS
Abstract We discuss ℓp-maximal regularity of power-bounded operators and relate the discrete to the continuous time problem for analytic semigroups. We give a complete characterization of operatorsExpand
BANACH SPACE OPERATORS WITH A BOUNDED H^∞ FUNCTIONAL CALCULUS
In this paper, we give a general definition for f(T) when T is a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent bounds, andExpand
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