Main Areas Harmonic Analysis and Function Spaces Overview of Research I use various methods to study connections between properties of functions and their Fourier transforms. For instance, in my 1997 paper in the Tohoku Mathematics Journal, I considered integrable functions on the real line with nonnegative transforms, and showed that such functions are squareintegrable in some neighbourhood of the origin if and only if More recent work along those lines is posted on arxiv.org in a joint paper with Walter Bloom and Michael Leinert. Sometimes my own methods do not satisfy me, and I return to a key instance where they worked, and reprove those conclusions in a different way that extends to new situations. My paper in the Pacific Journal of Mathematics in 1969 contains three proofs of a particular fact, two by known methods More recently, I returned to these issues once again, and was able to apply the method that was new in my thesis to other questions. See my papers the missing proof, noncommutative Khintchine and discrete Fourier restriction. 

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