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A Characterization of Some Sets of Spectral Synthesis
Journal of Fourier Analysis and Applications ( IF 1.2 ) Pub Date : 2021-03-02 , DOI: 10.1007/s00041-020-09805-y
Raymond Johnson , C. Robert Warner

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:

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。

更新日期:2021-03-02
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