The Hilbert transform H can be extended to an isometry of L^2. We prove this fact working directly on the principal value integral, completely avoiding the use of the Fourier transform and the use of orthogonal systems of functions. Our approach here is a byproduct of our attempts to understand the rearrangement properties of H.
A simple real-variable proof that the Hilbert transform is an L^2-isometry
LAENG, ENRICO
2010-01-01
Abstract
The Hilbert transform H can be extended to an isometry of L^2. We prove this fact working directly on the principal value integral, completely avoiding the use of the Fourier transform and the use of orthogonal systems of functions. Our approach here is a byproduct of our attempts to understand the rearrangement properties of H.File in questo prodotto:
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