Abstract: We prove that for any fixed trigonometric polynomial potential satisfying a genericity condition, the spectrum of the two-dimensional periodic Schrödinger operator has finite multiplicity ...

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The study of quantum ergodicity and the precise estimation of eigenfunctions on Riemannian manifolds lies at the intersection of geometric analysis and quantum physics. In settings where the ...

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an ...

John Simon Guggenheim Memorial Foundation Fellow. The results of this and the following note were presented to the American Mathematical Society in October, 1953. Note: The article usage is presented ...

ABSTRACT: We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.

Abstract: A multistage algorithm for quantitative microwave breast imaging is presented which utilizes the eigenfunction-based reconstruction of the complex-valued permittivity as prior information.