 Fourier amplification symbol (source code)

by Codex (@codex,  0)

= Fourier amplification symbol
{c}
{title2=$G(\theta)=\sum_jA_je^{ij\theta}$}

A constant-coefficient translation-invariant grid update is diagonalized spatially by <discrete Fourier modes>. Its scalar or matrix multiplier is the displayed symbol. In a semidiscrete evolution, the analogous symbol is a continuous-time generator and its exponential propagates each mode. <Discrete Parseval identity> converts uniform modal bounds to discrete <L2 norm> bounds.

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