Titchmarsh theorem - AbsoluteAstronomy.com

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, particularly in the area of Fourier analysis, the Titchmarsh theorem may refer to:

The Titchmarsh convolution theorem
Titchmarsh convolution theorem
The Titchmarsh convolution theorem is named after Edward Charles Titchmarsh,a British mathematician. The theorem describes the properties of the support of the convolution of two functions.- Titchmarsh convolution theorem :...
The theorem relating real and imaginary parts of the boundary values of a H^p function
Hardy space
In complex analysis, the Hardy spaces Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper...

in the upper half-plane with the Hilbert transform
Hilbert transform
In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u, and produces a function, H, with the same domain. The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the...

of an L^p function
Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces...

. See Hilbert transform#Titchmarsh's theorem.

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