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Almost periodic function
(section)
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===Weyl almost periodic functions=== The space ''W''<sup>''p''</sup> of Weyl almost periodic functions (for ''p'' β₯ 1) was introduced by Weyl (1927).<ref>H. Weyl, "Integralgleichungen und fastperiodische Funktionen" Math. Ann., 97 (1927) pp. 338β356</ref> It contains the space ''S''<sup>''p''</sup> of Stepanov almost periodic functions. It is the closure of the trigonometric polynomials under the seminorm :<math>\|f\|_{W,p}=\lim_{r\to\infty}\|f\|_{S,r,p}</math> Warning: there are nonzero functions ''ƒ'' with ||''ƒ''||<sub>''W'',''p''</sub> = 0, such as any bounded function of compact support, so to get a Banach space one has to quotient out by these functions.
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