scholarly journals Functional calculus on real interpolation spaces for generators ofC0-groups

2015 ◽  
Vol 289 (2-3) ◽  
pp. 275-289 ◽  
Author(s):  
Markus Haase ◽  
Jan Rozendaal
Keyword(s):  
Functional Calculus ◽  
Real Interpolation ◽  
Interpolation Spaces

scholarly journals The absolute functional calculus for sectorial operators

2005 ◽  
Author(s):  
◽  
Tamara Kucherenko
Keyword(s):  
Functional Calculus ◽  
Maximal Regularity ◽  
Real Interpolation ◽  
Future Research ◽  
Interpolation Spaces ◽  
Holomorphic Functional Calculus ◽  
Sectorial Operators ◽  
The Common ◽  
The Absolute ◽  
Key Theorem

We introduce the absolute functional calculus for sectorial operators. This notion is stronger than the common holomorphic functional calculus. We are able to improve a key theorem related to the maximal regularity problem and hence demonstrate the power and usefulness of our new concept. In trying to characterize spaces where sectorial operators have absolute calculus, we find that certain real interpolation spaces play a central role. We are then extending various known results in this setting. The idea of unifying theorems about sectorial operators on real interpolation spaces permeates our work and opens paths for future research on this subject.

scholarly journals Functional Calculus on Real Interpolation Spaces for the Series Generators of C_0-groups

2019 ◽  
Vol 11 (5) ◽  
pp. 52
Author(s):  
Simon Joseph ◽  
Manal Juma ◽  
Isra Mukhtar ◽  
Nagat Suoliman ◽  
Fatin Saeed
Keyword(s):  
Banach Space ◽  
Functional Calculus ◽  
Real Interpolation ◽  
Interpolation Spaces ◽  
Transference Principle

In this paper, discus functional calculus properties of C_0-groups on real interpolation spaces using transference principles. Obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then showed in (Markus, H., & Jan, R. 2016) that all group sequence of generators on a Banach space has a bounded H_0^∞-calculus on real interpolation spaces. Additional results are derived from this.

Ultraproducts of real interpolation spaces between Lp-spaces

2006 ◽  
Vol 37 (2) ◽  
pp. 191-216 ◽  
Author(s):  
J. A. López Molina ◽  
M. E. Puerta ◽  
M. J. Rivera
Keyword(s):  
Real Interpolation ◽  
Interpolation Spaces ◽  
Lp Spaces

Infinite Dimensional Geometric Properties of Real Interpolation Spaces

1998 ◽  
Vol 191 (1) ◽  
pp. 215-228 ◽  
Author(s):  
Denka Kutzarova ◽  
Lyudmila I. Nikolova ◽  
Stanislaw Prus
Keyword(s):  
Real Interpolation ◽  
Interpolation Spaces ◽  
Geometric Properties ◽  
Infinite Dimensional

scholarly journals On an extreme class of real interpolation spaces

2009 ◽  
Vol 256 (7) ◽  
pp. 2321-2366 ◽  
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera ◽  
Thomas Kühn ◽  
Tino Ullrich
Keyword(s):  
Real Interpolation ◽  
Interpolation Spaces

scholarly journals On continuity properties of semigroups in real interpolation spaces

2020 ◽  
Author(s):  
Peer Christian Kunstmann
Keyword(s):  
Banach Space ◽  
Schrodinger Equation ◽  
Continuous Semigroup ◽  
Stokes Equations ◽  
Nonlinear Schrodinger Equation ◽  
Real Interpolation ◽  
Navier Stokes ◽  
Interpolation Spaces ◽  
Navier Stokes Equations ◽  
Continuity Properties

AbstractStarting from a bi-continuous semigroup in a Banach space X (which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation spaces between X and the domain D(A) of the generator. Of particular interest is the case $$(X,D(A))_{\theta ,\infty }$$ ( X , D ( A ) ) θ , ∞ . We obtain topologies with respect to which the induced semigroup is bi-continuous, among them topologies induced by a variety of norms. We illustrate our results with applications to a nonlinear Schrödinger equation and to the Navier–Stokes equations on $$\mathbb {R}^d$$ R d .

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