# Article

Full entry | PDF   (0.2 MB)
Keywords:
orthogonal series; matrix summability
Summary:
In the paper, we prove two theorems on $|A, \delta |_{k}$ summability, $1\leq k\leq 2$, of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
References:
[1] Okuyama, Y.: On the absolute Nörlund summability of orthogonal series. Proc. Japan Acad. 54 (1978), 113-118. MR 0493132 | Zbl 0409.42004
[2] Okuyama, Y., Tsuchikura, T.: On the absolute Riesz summability of orthogonal series. Anal. Math. 7 (1981), 199-208. DOI 10.1007/BF01908522 | MR 0635485 | Zbl 0479.42008
[3] Tanaka, M.: On generalized Nörlund methods of summability. Bull. Austral. Math. Soc. 19 (1978), 381-402. DOI 10.1017/S0004972700008935 | MR 0536890 | Zbl 0425.40004
[4] Okuyama, Y.: On the absolute generalized Nörlund summability of orthogonal series. Tamkang J. Math. 33 (2002), 161-165. MR 1897504
[5] Flett, T. M.: On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. 7 (1957), 113-141. MR 0086912 | Zbl 0109.04402
[6] Flett, T. M.: Some more theorems concerning the absolute summability of Fourier series and power series. Proc. London Math. Soc. 8 (1958), 357-387. MR 0102693 | Zbl 0109.04502
[7] Lal, S.: Approximation of functions belonging to the generalized Lipschitz Class by $C^{1}\cdot N_{p}$ summability method of Fourier series. Appl. Math. Comput. 209 (2009), 346-350. DOI 10.1016/j.amc.2008.12.051 | MR 2493410 | Zbl 1159.42302

Partner of