Convergence of series of simple partial fractions in $ L_p(\mathbb R)$

DOI10.1070/SM2011V202N10ABEH004196zbMath1244.30003MaRDI QIDQ3225585

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Publication date: 22 March 2012

Published in: Sbornik: Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fourier transformHardy's inequalitysimple partial fractionsDirichlet series.

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Dirichlet series, exponential series and other series in one complex variable (30B50)

Related Items (12)

Approximation by linear fractional transformations of simple partial fractions and their differences ⋮ Extremal problems in geometric function theory ⋮ On convergence of series of simple partial fractions in \(L_p(\mathbb{R})\) ⋮ Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions ⋮ An example of non-uniqueness of a simple partial fraction of the best uniform approximation ⋮ Estimates of \(L_{p}\) norms for sums of positive functions ⋮ Extremal and approximative properties of simple partial fractions ⋮ Criteria for the best approximation by simple partial fractions on semi-axis and axis ⋮ Least deviation of logarithmic derivatives of algebraic polynomials from zero ⋮ Sharp quadrature formulas and inequalities between various metrics for rational functions ⋮ Estimates for \(L_p\)-norms of simple partial fractions ⋮ On the convergence of series in spaces of integrable functions

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