Representation of Fourier Integrals as Sums. Iip
نویسنده
چکیده
provided an = sin (wn/2) and k(x) =sin (irx/2). Weinberger [8] treated the case when the coefficients a„ form a periodic sequence; that is an+q = a„ for some integer q. Making use of the character theory of Dirichlet 7-functions, he found the conditions on the a„ so that (3) holds with the kernel (2/q112) cos (2irx/q) or the kernel (2/q112) sin (2irx/q). (These kernels give self-reciprocal transforms for any value of q.) Weinberger's proofs hold under essentially the same conditions on (p as given in I. Boas [l ] made use of Poisson's summation formula to obtain representation formulae of the type (1) and (2) together with certain generalizations. In this connection it is of interest to note that the following Poisson summation formula
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تاریخ انتشار 2010