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Calderón's Formula

f(x)=C_psiint_(-infty)^inftyint_(-infty)^infty<f,psi^(a,b)>psi^(a,b)(x)a^(-2)dadb,

where

psi^(a,b)(x)=|a|^(-1/2)psi((x-b)/a).

This result was originally derived using harmonic analysis, but also follows from a wavelets viewpoint.

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Cite this as:

Weisstein, Eric W. "Calderón's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CalderonsFormula.html

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