Re: [其他] Wiener class
※ 引述《handsomepow (handsomepow)》之銘言：
: 在書上看到
: Let f be a function in the Wiener class
: 也沒多加說明
: 網路上查 查不到講解 Wiener class的東西
: 想請教一下有沒有人知道這是什麼
A class of functions defined such that its p-variation is finite.
i.e. A class of bounded p-variation functions.
i.e.
Suppose a = t_0 < t_1 < ... < t_n = b be a partition of [a,b]
For 1 < p < +oo,
n 1/p
consider the quantity V_p(f) = sup{Σ | f(t_i) - f(t_{i-1}) |} < +oo
i=1
Vp = {f:[a,b]->|R | V_p(f) < +oo} is called the Wiener class on [a,b].
Sometimes, to connect with Fourier coeff., only consider the case on [0,2π].
[1] N. Wiener,
The quadratic variation of a function and its Fourier coefficients.
Massachusetts J. Math. 3(1924), 72–94.
[2] B. I. Golubov,
Continuous functions of bounded p-variation.
Mathematical Notes Volume 1, Number 3(1967), 203-207
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04/14 10:05, , 1F
04/14 10:05, 1F
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