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Summability of Fourier series in 
Author:
Marvin Rosenblum
Journal:
Trans. Amer. Math. Soc. 105 (1962), 32-42
MSC:
Primary 42.20
MathSciNet review:
0160073
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References |
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Additional Information
- [1]
K.
I. Babenko, On conjugate functions, Doklady Akad. Nauk SSSR
(N. S.) 62 (1948), 157–160 (Russian). MR 0027093
(10,249b)
- [2]
Arne
Beurling, On two problems concerning linear transformations in
Hilbert space, Acta Math. 81 (1948), 17. MR 0027954
(10,381e)
- [3]
Yung-ming
Chen, Theorems of asymptotic approximation, Math. Ann.
140 (1960), 360–407. MR 0112931
(22 #3777)
- [4]
R.
E. Edwards, The stability of weighted Lebesgue
spaces, Trans. Amer. Math. Soc. 93 (1959), 369–394. MR 0112050
(22 #2908), http://dx.doi.org/10.1090/S0002-9947-1959-0112050-4
- [5]
Erdélyi et al., Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.
- [6]
V.
F. Gapoškin, A generalization of the theorem of M. Riesz on
conjugate functions., Mat. Sb. N. S. 46(88) (1958),
359–372 (Russian). MR 0099561
(20 #6000)
- [7]
Ulf
Grenander and Gabor
Szegö, Toeplitz forms and their applications, California
Monographs in Mathematical Sciences, University of California Press,
Berkeley, 1958. MR 0094840
(20 #1349)
- [8]
G.
H. Hardy and J.
E. Littlewood, Some more theorems concerning Fourier series and
Fourier power series, Duke Math. J. 2 (1936),
no. 2, 354–382. MR
1545928, http://dx.doi.org/10.1215/S0012-7094-36-00228-4
- [9]
Henry
Helson and Gabor
Szegö, A problem in prediction theory, Ann. Mat. Pura
Appl. (4) 51 (1960), 107–138. MR 0121608
(22 #12343)
- [10]
I.
I. Hirschman, The decomposition of Walsh and Fourier series,
Mem. Amer. Math. Soc. 1955 (1955), no. 15, 65. MR 0072269
(17,257e)
- [11]
A. Zygmund, Trigonometric series. I, Cambridge, 1959.
- [12]
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge, 1952.
- [1]
- K. I. Babenko, On conjugate functions, Dokl. Akad. Nauk SSSR (N.S.) 62 (1948), 157-160. (Russian) MR 0027093 (10:249b)
- [2]
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. MR 0027954 (10:381e)
- [3]
- Y. Chen, Theorems of asymptotic approximation, Math. Ann. 140 (1960), 360-407. MR 0112931 (22:3777)
- [4]
- R. E. Edwards, The stability of weighted Lebesgue spaces, Trans. Amer. Math. Soc. 93 (1959), 369-394. MR 0112050 (22:2908)
- [5]
- Erdélyi et al., Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.
- [6]
- V. F. Gapoškin, A generalization of a theorem of M. Riesz on conjugate functions, Mat. Sb. 46 (88) (1958), 359-372. (Russian) MR 0099561 (20:6000)
- [7]
- V. Grenander and G. Szegö, Toeplitz forms and their applications, Univ. of Calif. Press, Berkeley and Los Angeles, 1958. MR 0094840 (20:1349)
- [8]
- G. H. Hardy and J. E. Littlewood, Some more theorems concerning Fourier series and Fourier power series, Duke Math. J. 2 (1936), 354-382. MR 1545928
- [9]
- H. Helson and G. Szegö, A problem in prediction theory, Ann. Mat. Pura Appl. (IV) 51 (1960), 107-138. MR 0121608 (22:12343)
- [10]
- I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. No. 15 (1955). MR 0072269 (17:257e)
- [11]
- A. Zygmund, Trigonometric series. I, Cambridge, 1959.
- [12]
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge, 1952.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1962-0160073-1
PII:
S 0002-9947(1962)0160073-1
Article copyright:
© Copyright 1962 American Mathematical Society
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