On the Fourier coefficients of homeomorphisms of the circle
On the Fourier coefficients of homeomorphisms of the circle
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关于圆同胚的傅立叶系数
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发表时间：
1998
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通讯作者：
Allen Weitsman
中科院分区：
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作者：
Allen Weitsman
其中ω(t+j)和ω(t−j)分别表示右极限和左极限。我们将把这些同胚f的极限，即对应于2个π周期函数e且ω增加但不一定连续的极限称为伪同胚。本文将证明定理1.设ω(S)是一个非减函数，具有e2π周期，ω(2π)=ω(0)+2π)，并且具有傅立叶展开(1.1)。然后
where ω(t+j ) and ω(t − j ) denote right and left limits respectively. We shall refer to the limits of these homeomorphisms f , that is those corresponding to 2πperiodic functions e with ω increasing but not necessarily continuous, as pseudohomeomorphisms. In this paper we shall prove Theorem 1. Let ω(s) be a nondecreasing function with e 2π-periodic, ω(2π) = ω(0) + 2π, and having Fourier expansion (1.1). Then