On regular matrices that induce the Gibbs phenomenon
Proc. Amer. Math. Soc. 25 (1970), 481-487
Primary 40.31; Secondary 42.00
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Abstract: Let be a sequence of complex valued functions defined in a subset of the complex plane and suppose that converges to for . For let and be the cores of and respectively. We say that does not have the Gibbs phenomenon at if . The regular matrix is said to induce the Gibbs phenomenon in if but . We characterize those regular matrices that induce the Gibbs phenomenon.
Atalla and J.
Bustoz, On sequential cores and a theorem of
R. R. Phelps, Proc. Amer. Math. Soc. 21 (1969), 36–42. MR 0243357
(39 #4679), http://dx.doi.org/10.1090/S0002-9939-1969-0243357-X
G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan
& Co., Ltd., London, 1950. MR 0040451
W. A. Hurwitz, Some properties of methods of evaluation of divergent sequences. Proc. London Math. Soc. (2) 26 (1927), 231-248.
Izumi and Masako
Satô, Fourier series. X. Rogosinski’s lemma,
Kōdai Math. Sem. Rep. 8 (1956), 164–180. MR 0086179
- R. Atalla and J. Bustoz, On sequential cores and a theorem of R. R. Phelps, Proc. Amer. Math. Soc. 21 (1969), 36-42. MR 0243357 (39:4679)
- R. G. Cooke, Infinite matrices and sequence spaces, Macmillan, New York, 1950; reprint, Dover, New York, 1955. MR 12, 694. MR 0040451 (12:694d)
- W. A. Hurwitz, Some properties of methods of evaluation of divergent sequences. Proc. London Math. Soc. (2) 26 (1927), 231-248.
- S. Izumi and M. Satô, Fourier series. : Rogosinski's Lemma, Kōdai Math. Sem. Rep. 8 (1956), 164-180. MR 19, 138. MR 0086179 (19:138c)
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