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 \(d \ge 1\).

中文翻译：

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几套光谱合成的特征

我将描述与已故的鲍勃·华纳（Bob Warner）的共同工作。我们知道\（H ^ 1（R）\）对于奇异积分的结果要好于\（L ^ 1（R）\） ; 我们的问题是：光谱合成是否也是如此？。我们扩展了Beurling–Pollard参数，为\（H ^ 1（R）\）中的频谱合成提供了充分的条件。我们激励和构造一类Q满足合成的边界和工会财产-scets，并给出的例子Q（套）。在某种程度上，该论点的技术部分扩展到\（d \ ge 1 \）的d维欧几里得空间。