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Start Over Subject double sine series

1. On the behavior near the origin of double sine series with monotone coefficients

Creator:
Krasniqi, Xhevat Z.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
double sine series and sum of a double sine series with monotone coefficients
Language:
English
Description:
In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients ak,l satisfy certain conditions) the following order equality is proved g(x,y) ∼ mnam,n + m⁄ n ∑ n−1 l=1 lam,l + n⁄ m ∑mX−1 k=1 kak,n + 1 m ⁄n ∑ n−1 l=1 ∑ m−1 k=1 klak,l, where x ∈ ( π⁄ m+1 , π ⁄ m ], y ∈ ( π ⁄ n+1 , π ⁄ n ], m, n = 1, 2, . . ..
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Uniform convergence of double trigonometric series

Creator:
Kórus, Péter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
sine series, cosine series, double sine series, sine-cosine series, double cosine series, uniform convergence, regular convergence, general monotone sequence, general monotone double sequence, and supremum bounded variation
Language:
English
Description:
It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone or general monotone double sequences. In this paper we give new sufficient conditions for the uniformity of the regular convergence of sine-cosine and double cosine series, which are necessary as well in case the coefficients are non-negative. The new results also bring necessary and sufficient conditions for the uniform regular convergence of double trigonometric series in complex form.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public