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Award ID contains: 1814253

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  1. ; (, Sampling Theory, Signal Processing, and Data Analysis)
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  2. ; ; (, Communications in Partial Differential Equations)
    null (Ed.)
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  3. ; ; ; ; (, Advances in Computational Mathematics)
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  4. ; ; (, Demonstratio Mathematica)
    Abstract We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite fractal sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular we permit both the fractal Laplacian and the potential to be Radon measures on the fractal. As a consequence of our results, we establish a Harnack inequality for solutions of these operators. 
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  5. (, Journal of Fourier Analysis and Applications)
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  6. ; ; (, Journal of Fourier Analysis and Applications)
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  7. (, Notices of the American Mathematical Society)
    Gabor analysis, which can be traced back to Dennis Gabor's influential 1946 paper "Theory of communication," is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of a given window function. It re-emerged with the advent of wavelets at the end of the last century and is now at the intersection of many fields of mathematics, applied mathematics, engineering, and science. The goal of this paper is to give a brief introduction to Gabor analysis by elaborating on three open problems. 
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