By T. Christiansen and K. Datchev

Using coordinates *(x,y)\in \mathbb R\times \mathbb R^{d-1}*, we introduce the notion that an unbounded domain in *\mathbb R^d* is star shaped with respect to *x=\pm \infty*. For such domains, we prove estimates on the resolvent of the Dirichlet Laplacian near the continuous spectrum. When the domain has infinite cylindrical ends,... Show more

June 7, 2021

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Resolvent estimates, wave decay, and resonance-free regions for star-shaped waveguides

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