Lutz Weis
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View article: Euclidean Structures and Operator Theory in Banach Spaces
Euclidean Structures and Operator Theory in Banach Spaces Open
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators on a Hilbert space. Our assumption on is expressed in terms of -boundedness for a…
View article: Euclidean structures and operator theory in Banach spaces
Euclidean structures and operator theory in Banach spaces Open
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $Γ$ on a Hilbert space. Our assumption on $Γ$ is expressed in terms of $α$-boundedn…
View article: Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds
Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds Open
We prove pathwise uniqueness for solutions of the nonlinear Schrödinger equation with conservative multiplicative noise on compact 3D manifolds. In particular, we generalize the result by Burq, Gérard and Tzvetkov (N. Burq, P. Gérard, and …
View article: Spectral multiplier theorems via $H^\infty$ calculus and $R$-bounds
Spectral multiplier theorems via $H^\infty$ calculus and $R$-bounds Open
We prove spectral multiplier theorems for Hörmander classes $\mathcal{H}^α\_p$ for 0-sectorial operators A on Banach spaces assuming a bounded $H^\infty(Σ\_σ)$ calculus for some $σ\in (0,π)$ and norm and certain R-bounds on one of the foll…
View article: Paley-Littlewood decomposition for sectorial operators and interpolation spaces
Paley-Littlewood decomposition for sectorial operators and interpolation spaces Open
We prove Paley-Littlewood decompositions for the scales of fractional powers\nof $0$-sectorial operators $A$ on a Banach space which correspond to\nTriebel-Lizorkin spaces and the scale of Besov spaces if $A$ is the classical\nLaplace oper…