This $335,000 project grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in harmonic analysis and approximation theory conducted by the University of Wisconsin - Madison. The key objectives are to:
(1) Investigate the regularity properties and boundedness of certain averaging operators over sub-manifolds and maximal operators on nilpotent groups within harmonic analysis.
(2) Study local smoothing phenomena for wave equation solutions with restricted dilation sets, examining the impact of different notions of dimension.
(3) Pursue projects on sparse domination and endpoint estimates in harmonic analysis, leveraging atomic decomposition techniques.
(4) Characterize approximation spaces for nonlinear wavelet approximation, focusing on high-order approximation where the spaces are not normed.
The project aims to expand the mathematical toolbox in harmonic analysis and contribute to a deeper theoretical understanding with potential applications in the natural sciences and engineering. The award also supports the mentoring of graduate students as an important educational component. No subawards are planned under this grant, which has an ultimate completion date of August 31, 2027.
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