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Trilinear Hilbert Transform

The trilinear Hilbert transform is a singular integral that multiplies three inputs translated at distinct fixed rates before integration against dt/t. For the slopes 1, 2, and 3, it is

T(f_1,f_2,f_3)(x)=PVintRf_1(x-t)f_2(x-2t)f_3(x-3t)(dt)/t,

initially for complex functions in the Schwartz space. The Cauchy principal value removes a symmetric interval about zero.

The triangular Hilbert transform has two inputs on R^2 and is a different operator.

See also

Cauchy Principal Value, Hilbert Transform, Schwartz Function, Singular Integral, Triangular Hilbert Transform

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References

Durcik, P. and Thiele, C. "Singular Brascamp-Lieb: A Survey." In Geometric Aspects of Harmonic Analysis (Ed. P. Ciatti and A. Martini). Cham, Switzerland: Springer, pp. 321-349, 2021. https://doi.org/10.1007/978-3-030-72058-2_9.

Cite this as:

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

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