Convolution kernels of 2D Fourier multipliers based on real analytic\n functions

2016/05/25 by Michael Greenblatt, Greenblatt, Michael
Computer Science · Mathematics · #42B15 #42B20 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1605.08136

openalex publication_date 2016/05/25 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper, estimates are proven for convolution kernels associated to\nmultipliers from a reasonably general class of compactly supported\ntwo-dimensional functions constructed out of real-analytic functions. These\nestimates are both for overall decay rate and decay rate in specific\ndirections. The estimates are sharp for a certain range of exponents appearing\nin the theorems.\n

Related

• Estimates for Fourier sums and eigenvalues of integral operators via multipliers on the sphere
• Convolution powers of complex functions on Z
• Estimates of convolution operators of functions from L_2π^p(x)
• Fourier transforms of powers of well-behaved 2D real analytic functions
• Initial L²×⋯× L² bounds for multilinear operators