1 citations · 1 across the 7 of their papers we have counts for
13 papers
Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
For periodic Schrödinger operators with bounded real-valued potentials on with , we show that for generic potentials, each endpoint of every spectra…
Generic twisted Pollicott--Ruelle resonances and zeta function at zero
Tristan Humbert, Zhongkai Tao
For a connected orientable closed surface of genus with Anosov geodesic flow, we show the existence of an open subset of finite-dimensional irreducible representa…
Polynomial bounds for eigenfunctions and eigenvalues on random covers of hyperbolic surfaces
Elena Kim, Zhongkai Tao
Let be a compact connected orientable hyperbolic surface and let be a degree cover, taken uniformly at random. We show that, with high probability, the nor…
Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory
Philip Isett, Yuchen Mao, Sung-Jin Oh +1
We introduce a new versatile method for constructing solution operators (i.e., right-inverses up to a finite rank operator) for a wide class of underdetermined PDEs , whic…
Wannier decay and the Thouless conjecture
Simon Becker, Zhongkai Tao, Mengxuan Yang
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch…
Lossless Strichartz and spectral projection estimates on unbounded manifolds
Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao +1
We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order…