Open AccessOn $ (J, p_n) $ summability of fourier series
Author(s) -
Sulekh Chandra
Publication year - 2001
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.32.2001.378
Subject(s) - mathematics , fourier series , series (stratigraphy) , combinatorics , fourier transform , pi , mathematical analysis , geometry , paleontology , biology
In this paper we prove the following two theorems for $ | J, p_n | $ summability of fourier series, which generalizes many previous result:
Theorem 1. If
$$ Phi (t) = int_t^{pi} frac{phi (u)}{u} du = o { p (1- frac{1}{t} ) } ~~~~ (t o 0) $$
then the Fourier series for $ t = x $ is summable $ (J, p_n) $ to sum $ s $.
Theorem 2. If
$$ G(t) = int_t^{pi} frac{g(u)}{u} du = o { p(1-frac{1}{t}) } ~~~~ (t o 0) $$
then the differentiated Fourier series is summable $ (J, p_n) $ to the value $ C $.