Dimension estimates for vectorial measures with restricted spectrum
Dmitriy Stolyarov
TL;DR
This paper connects the problem of estimating the lower Hausdorff dimension of measures constrained by PDEs or Fourier conditions with Harnack's inequalities for the heat equation, offering new estimates especially for Fourier-constrained measures.
Contribution
It introduces a novel approach linking dimension estimates with Harnack's inequalities, providing new bounds for Fourier-constrained measures.
Findings
New estimates for the lower Hausdorff dimension of Fourier-constrained measures
Established a connection between PDE constraints and measure dimension
Enhanced understanding of measure properties under spectral restrictions
Abstract
We link the problem of estimating the lower Hausdorff dimension of PDE or Fourier constrained measures with Harnack's inequalities for the heat equation. Our approach provides new estimates in the case of Fourier constraints.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · advanced mathematical theories