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On finite configurations in the spectra of singular measures - MaRDI portal

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On finite configurations in the spectra of singular measures

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Publication:6376109

DOI10.1007/S00209-023-03257-YarXiv2108.12036MaRDI QIDQ6376109

Author name not available (Why is that?)

Publication date: 26 August 2021

Abstract: We establish various forms of the following certainty principle: a set SsubsetmathbbRn contains a given finite linear pattern, provided that S is a support of the Fourier transform of a sufficiently singular probability measure on mathbbRn. As its main corollary, we provide new dimensional estimates for PDE- and Fourier-constrained vector measures. Those results, in certain cases of restrictions given by homogeneous operators, improve known bounds related to the notion of the k-wave cone.





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