Abstract
I will describe joint work with the late Bob Warner. We knew that \(H^1(R)\) gave better results for singular integrals than \(L^1(R)\); our question was: Would the same be true for spectral synthesis?. We extend the Beurling–Pollard argument to give sufficient conditions for spectral synthesis in \(H^1(R)\). We motivate and construct a class of Q-scets which satisfy the boundary and union property of synthesis, and give examples of Q-sets. To some extent the technical parts of the argument extend to d-dimensional Euclidean spaces for \(d \ge 1\).
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Communicated by John Benedetto.
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C. Robert Warner: Deceased.
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Johnson, R., Warner, C.R. A Characterization of Some Sets of Spectral Synthesis. J Fourier Anal Appl 27, 11 (2021). https://doi.org/10.1007/s00041-020-09805-y
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DOI: https://doi.org/10.1007/s00041-020-09805-y