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Displaying 761 – 780 of 1346

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

Let $a ₁, . . ., a_{k}$ be arbitrary nonzero real numbers. An $(a ₁, . . ., a_{k})$ -decomposition of a function f:ℝ → ℝ is a sum $f ₁ + \dots + f_{k} = f$ where $f_{i} : ℝ \to ℝ$ is an $a_{i}$ -periodic function. Such a decomposition is not unique because there are several solutions of the equation $h ₁ + \dots + h_{k} = 0$ with $h_{i} : ℝ \to ℝ a_{i}$ -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the $(a ₁, . . ., a_{k})$ -decomposition is essentially unique. We characterize those periods for which essential uniqueness...

On the utility of the Telyakovskiĭ's class $S$ .

Leindler, L. (2001)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the variance of the number of real roots of a random trigonometric polynomial.

Farahmand, K. (1990)

Journal of Applied Mathematics and Stochastic Analysis

On the weak $L^{1}$ space and singular measures

Robert Kaufman (1982)

Annales de l'institut Fourier

We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak $L^{1}$ space; symmetric sets of constant ratio occur in an unexpected way.

On the weighted estimate of the Bergman projection

Benoît Florent Sehba (2018)

Czechoslovak Mathematical Journal

We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.