Fourier transforms of rapidly decreasing functionsстатья
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Аннотация:If f is an element of L-p(R), p greater than or equal to 2, then the Fourier transform F(z) of the function exp(-alpha\t\(alpha))f(t), alpha > 0, alpha > 1, belongs to the space of entire functions that are p-power integrable over the whole plane with some completely determined weight. Conversely, if F(z) is an entire function in such a space, where 1 less than or equal to p less than or equal to 2, then F(z) is a Fourier transform of the above form for some function f is an element of L-p(R).