Positive trigonometric sums and applications.
Power-monotone sequences and Fourier series with positive coefficients.
Power-monotone sequences and Fourier series with positive coefficients.
Power-monotone sequences and integrability of trigonometric series.
Refinement Equations with Nonnegative Coefficients.
Representations Of Monotonic Fourier Coefficients In Tauberian L1-Convergence Classes
Sidon Type Inequalities
Some new modified cosine sums and -convergence of cosine trigonometric series
In this paper we introduce some new modified cosine sums and then using these sums we study -convergence of trigonometric cosine series.
Some remarks an interpolation of operators and Fourier coefficients
Sur le minimum d'une somme de cosinus
Sur les coefficients des séries de Fourier dont les sommes partielles sont positives sur un ensemble
Sur les espaces de Fréchet ne contenant pas
Soit E un espace de Fréchet séparable ne contenant pas ; soit de plus une suite symétrique de vecteurs aléatoires à valeurs dans E. Alors si la série de Fourier aléatoire , , a p.s. ses sommes partielles localement uniformément bornées dans E, nécessairement elle converge p.s. uniformément sur tout compact de vers une fonction aléatoire à valeurs dans E et à trajectoires continues.
Sur une série trigonométrique particulière
Tauberian conditions for -convergence of modified complex trigonometric sums.
The Fourier Character Of Series With Slowly Varying Convergence Moduli
Trigonometric series with -monotone coefficients in spaces with mixed quasinorm.
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen
Uniform convergence of double trigonometric series
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...
Weighted integrability of double cosine series with nonnegative coefficients
Let with for all j,k ≥ 1. We estimate the integral in terms of the coefficients , where α, β ∈ ℝ and ϕ: [0,∞] → [0,∞]. Our results can be regarded as the trigonometric analogues of those of Mazhar and Móricz [MM]. They generalize and extend Boas [B, Theorem 6.7].