Absolute Nörlund summability almost everywhere of orthogonal series

1984 ◽  
pp. 24-36
Author(s):  
Yasuo Okuyama
Keyword(s):  
Orthogonal Series ◽  
Almost Everywhere ◽  
Absolute Nörlund Summability

On the Absolute Summability of Series with Respect to Block-Orthonormal Systems

1999 ◽  
Vol 6 (1) ◽  
pp. 83-90
Author(s):  
G. Nadibaidze
Keyword(s):  
Orthogonal Series ◽  
Absolute Summability ◽  
Almost Everywhere ◽  
Weyl Multiplier ◽  
The Absolute

Abstract Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {ω(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {Nk } such that {ω(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the Δ k -orthonormal systems.

scholarly journals On the Convergence and Summability of Series with Respect to Block-Orthonormal Systems

1995 ◽  
Vol 2 (5) ◽  
pp. 517-534
Author(s):  
G. Nadibaidze
Keyword(s):  
Orthogonal Series ◽  
Almost Everywhere

Abstract Statements connected with the so-called block-orthonormalized systems are given. The convergence and summability almost everywhere by the (c, 1) method with respect to such systems are considered. In particular, the well-known theorems of Menshov-Rademacher and Kacmarz on the convergence and (c,1)-summability almost everywhere of orthogonal series are generalized.

scholarly journals ON ABSOLUTE NORLUND SUMMABILITY OF ORTHOGONAL SERIES

1998 ◽  
Vol 29 (4) ◽  
pp. 245-247
Author(s):  
ABDULCABBAR SONMEZ
Keyword(s):  
Orthogonal Series ◽  
General Theorem ◽  
Absolute Nörlund Summability

The purpose of this paper is to give a general theorem on the $|N_{,p_n};\delta|_k$ summability of orthogonal series, which generalizes a theorem due to Okuyama [1] related to summability of orthogonal series.

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