Volume 3,  Issue 1, 2002

Article 10

SOME RESULTS ON L1 APPROXIMATION OF THE r-TH DERIVATE OF FOURIER SERIES

ZIVORAD TOMOVSKI

FACULTY OF MATHEMATICAL AND NATURAL SCIENCES
STS. CYRIL AND METHODIUS UNIVERSITY
PO BOX 162, 91000 SKOPJE
MACEDONIA.
E-Mail: tomovski@iunona.pmf.ukim.edu.mk

Received 22 September, 1999; Received in final form: 17 October, 2001, Accepted 18 October, 2001.
Communicated by: A.G. Babenko


ABSTRACT.   In this paper we obtain the conditions for L1-convergence of the r-th derivatives of the cosine and sine trigonometric series. These results are extensions of corresponding Sidon's and Telyakovskii's theorems for trigonometric series (case: r = 0).
Key words:
L1-approximation, Fourier series, Sidon-Telyakovskii class, Telyakovskii inequality.

2000 Mathematics Subject Classification:
26D15, 42A20.


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