$ \DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}} $

Homogenization in Translation invariant periodic spaces

This project aims to investigate the discretization of elliptic partial differential equations with periodic boundary conditions on anisotropic spaces of translates. Of special interest are the influence of the anisotropic sampling lattice, the choice of the translation invariant space, convergence results and the investigation of periodic wavelets. (missing reference)(missing reference)

References

    [1]

    1. Publication illustration image
      Bergmann, R and Merkert, D (2017). Approximation of periodic PDE solutions with anisotropic translation invariant spaces. 2017 International Conference on Sampling Theory and Applications (SampTA). 396–9

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