Zobrazeno 1 - 10
of 164
pro vyhledávání: '"Borthwick, David"'
On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends only on th
Externí odkaz:
http://arxiv.org/abs/2301.07149
We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and Schrader,
Externí odkaz:
http://arxiv.org/abs/2204.06619
Autor:
Borthwick, David, Wang, Yiran
Publikováno v:
Analysis & PDE 17 (2024) 2077-2108
We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions and asympto
Externí odkaz:
http://arxiv.org/abs/2110.06370
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 March 2024 531(1) Part 2
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.
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Externí odkaz:
http://arxiv.org/abs/1905.03071
We consider the focusing nonlinear Schr\"odinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing off the flat Euclidean case. Furthermore, we study the stability of th
Externí odkaz:
http://arxiv.org/abs/1809.07643
We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\delta$ of its limit set. More precisely, we show that as $R\to\infty$, the number of res
Externí odkaz:
http://arxiv.org/abs/1512.00836