Fourier spectrum characterization of Hardy Space
نویسنده
چکیده
Fourier spectrum of the boundary values of functions in the complex Hardy Space H(C+) is characterized for p ∈ (0, 2). First, functions f in the L(R) can be decomposed into a sum g + h, where g and h are the non-tangential boundary limits of function in H(C+) and H(C−) in the sense of L(R), where H(C+) and H(C−) are the Hardy spaces in the upper and lower complex plane C+ and C−, respectively. Secondly, as an application, extend the Paley-Wiener Theorem is extended, originally for square-integrable functions, to the H(C+) cases with 0 < p < 2. Finally, Fourier spectrum characterization is given for L(R) functions.
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