Fourier analysis on compact symmetric space

Fourier Analysis on Semisimple Symmetric Spaces

A homogeneous space X = G/H of a connected Lie group G is called a symmetric homogeneous space if there exists an involution σ of G such that H lies between the fixed point group G and its identity component Go . Example 0. For a connected Lie group G′, put G = G′×G′, σ(g1, g2) ) = (g2, g1) and H = G. Then the homogeneous space X = G/H is naturally isomorphic to G′ by the map (g1, g2) 7→ g1g−1 ...

On the Fourier transform for a symmetric group homogeneous space

By using properties of the Young orthogonal representation, this paper derives a simple form for the Fourier transform of permutations acting on the homogeneous space of n-dimensional vectors, and shows that the transform requires 2n− 2 multiplications and the same number of additions.

Fourier Integral Operators and Harmonic Analysis 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...

Compact Fourier Analysis for Designing Multigrid Methods

The convergence of Multigrid methods can be analyzed based on a Fourier analysis of the method or by proving certain inequalities that have to be fulfilled by the smoother and by the coarse grid correction separately. Here, we analyze the Multigrid method for the constant coefficient Poisson equation with a compact Fourier analysis using the formalism of multilevel Toeplitz matrices and their g...