Fourier multipliers, symbols, and nuclearity on compact manifolds

Compact Fourier Analysis for Multigrid Methods based on Block Symbols

The notion of Compact Fourier Analysis (CFA) is discussed. The CFA allows description of multigrid (MG) in a nutshell and offers a clear overview on all MG components. The principal idea of CFA is to model the MG mechanisms by means of scalar generating functions and matrix functions (block symbols). The formalism of the CFA approach is presented by describing the symbols of the fine and coarse...

Cubature formulas and discrete fourier transform on compact manifolds

Analysis on two dimensional surfaces and in particular on the sphere S found many applications in computerized tomography, statistics, signal analysis, seismology, weather prediction, and computer vision. During last years many problems of classical harmonic analysis were developed for functions on manifolds and especially for functions on spheres: splines, interpolation, approximation, differe...

Fourier Integral Operators and Harmonic Analysis On Compact Manifolds

Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1 < p < ∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.

Stable Sampling and Fourier Multipliers

We study the relationship between stable sampling sequences for bandlimited functions in Lp(Rn) and the Fourier multipliers in Lp. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship. 2010 Mathematics Subject Classification: 42A45, 42B15, 42C15, 62...