Linear Truncations of the Hilbert Transform
نویسنده
چکیده
where the integral in (1.1) should be interpreted in the principal value sense when (ax + b)(ax + d) < 0. Note that for a = 0, Ha,b,d is not a convolution operator. When a = 1, H1,b,d = H(fχ[−d,−b]) is the Hilbert transform composed with multiplication by the characteristic function of the interval [−d,−b]. When a = 0, H0,b,d is a well understood operator. In the sequel, we will concentrate our attention to a = 0, 1.
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