×

On the uniqueness of summable trigonometric series and integrals. (English) Zbl 0224.42008


MSC:

42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A50 Conjugate functions, conjugate series, singular integrals
42A24 Summability and absolute summability of Fourier and trigonometric series
41A40 Saturation in approximation theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrienko, V. A., O približenii funkcij srednimi Fejera, Sib. Mat. Žurn., 9, 3-11 (1968) · Zbl 0162.08701
[2] Berens, H., On the approximation of Fourier series by Abel means. (To appear). · Zbl 0262.42010
[3] Carleson, L., Selected problems on exceptional sets (1967), Princeton: Van Nostrand, Princeton · Zbl 0189.10903
[4] Saks, S.,Theory of the integral. Monografie matematyczne, Warsaw 1937. · JFM 63.0183.05
[5] Schwartz, L., Théorie des distributions (1950), Paris: Hermann, Paris · Zbl 0037.07301
[6] Shapiro, H. S., Smoothing and approximation of functions (1969), New York: Van Nostrand, New York · Zbl 0194.09101
[7] Shapiro, V. L., Cantor-type uniqueness of multiple trigonometric integrals, Pac. J. Math., 5, 607-622 (1955) · Zbl 0066.05002
[8] Shapiro, V. L., Uniqueness of multiple trigonometric series, Ann. Math., 66, 467-480 (1957) · Zbl 0089.27806 · doi:10.2307/1969904
[9] Shapiro, V. L., Fourier series in several variables, Bull. Amer. Math. Soc., 70, 48-93 (1964) · Zbl 0267.42011 · doi:10.1090/S0002-9904-1964-11026-0
[10] Sunouchi, G.; Butzer; Korevaar, Saturation in the theory of best approximation, On approximation theory. Proceedings of a Conference at Oberwolfach (1964), Basel: Birkhäuser, Basel · Zbl 0158.05601
[11] Verblunsky, S., On the theory of trigonometric series. II, Proc. London Math. Soc., 34, 457-491 (1932) · Zbl 0006.25603 · doi:10.1112/plms/s2-34.1.457
[12] Verblunsky, S., On trigonometric integrals and harmonic functions, Proc. London Math. Soc., 38, 1-48 (1935) · JFM 60.1002.02 · doi:10.1112/plms/s2-38.1.1
[13] Zygmund, A., Trigonometric series. I (1959), Cambridge: Cambridge University Press, Cambridge · Zbl 0085.05601
[14] Zygmund, A., Sur les séries trigonométriques sommables par le procédé de Poisson, Math. Z., 25, 274-290 (1926) · JFM 52.0272.02 · doi:10.1007/BF01283837
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.