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Triangular Hilbert Transform


The triangular Hilbert transform is a bilinear singular integral whose two inputs are translated in distinct coordinate directions. For complex functions F and G on R^2, its finite hard truncations are

 B_(epsilon,R)(F,G)(x,y)=int_(epsilon<|t|<R)F(x+t,y)G(x,y+t)(dt)/t,

where 0<epsilon<R<infty. Pairing the output with a third input gives a trilinear form with three equal L^3 exponents at the symmetric point.


See also

Dyadic Triangular Hilbert Form, Hilbert Transform, Singular Integral, Trilinear Hilbert Transform

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References

Kovač, V.; Thiele, C.; and Zorin-Kranich, P. "Dyadic Triangular Hilbert Transform of Two General Functions and One Not Too General Function." Forum Math. Sigma 3, e25, 2015. https://doi.org/10.1017/fms.2015.25.

Cite this as:

Weisstein, Eric W. "Triangular Hilbert Transform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TriangularHilbertTransform.html

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