Approximation by multivariate quasi-projection operators and Fourier\n multipliers

2020/06/23 by Yurii Kolomoitsev, Kolomoitsev, Yurii, M. Skopina +1 · 1 citation
Mathematics · #Mathematical Approximation and Integration #Approximation Theory and Sequence Spaces #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2006.13272

Abstract

Multivariate quasi-projection operators Q_j(f,\φ,\n widetilde\φ), associated with a function \φ and a\ndistribution/function widetilde\φ, are considered. The function\n\φ is supposed to satisfy the Strang-Fix conditions and a compatibility\ncondition with widetilde\φ. Using technique based on the Fourier\nmultipliers, we studied approximation properties of such operators for\nfunctions f from anisotropic Besov spaces and L_p spaces with 1\≤ p\≤\n\∞. In particular, upper and lower estimates of the L_p-error of\napproximation in terms of moduli of smoothness and best approximations are\nobtained.\n

Cited by

• Special measures of smoothness for approximation by sampling operators in L_p(ℝ^d)

Related

• Uniform approximation by multivariate quasi-projection operators
• Approximation by periodic multivariate quasi-projection operators
• Approximation properties of periodic multivariate quasi-interpolation\n operators
• Approximation by quasi-interpolation operators and Smolyak's algorithm
• Approximation of conjugate functions by general linear operators of\n their Fourier series at the Lebesgue points