Let r,1p={f:fr-1 is abs. cont. on I=[a, b], f is periodie with period H（=b-a）,f（x1）=0,‖f（r）‖p≤0}, where x1 is any fixed point in [a, b]. The author finds the Kolmogorov, Gel’land, linear, and Berustein n-widths of r,1p in Lp（I） for n odd, ∞p1. The optimal subspaces and operators are also found.
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