Research Interests
I work in Fourier analysis , or more generally harmonic analysis, and applications . I am interested in singular integrals and
Calderón-Zygmund operators, function spaces,
Littlewood-Paley theory, discrete decompositions, and wavelets.
Applications of this theoretical research
include partial differential equations and signal analysis .
I am also involved in interdisciplinary work in the
spectral analysis of nanostructures in biological tissues.
In general terms, Fourier analysis is a mathematical tool that permits the decomposition of a function or signal into a combination of oscillating waves of different frequencies and amplitudes, very much in the same way that a prism separates a beam of light into a rainbow of colors of different wavelengths. Fourier analysis and related mathematical techniques decode information present in signals or sets of data and provide a precise mechanism and quantitative way to analyze variations, oscillations, and sudden changes in the data, as well as trends, patterns, and symmetries.
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