Sampling theorem for not necessarily finite energy signals

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Abstract
This paper is intended to answer a recent question raised concerning the necessity for ‘a new mode of proof ’ for the sampling theorem. This relates to band limited functions with Fourier transform which is absolutely integrable but not square integrable. The method we present here makes use of Hölder inequality, as opposed to its special case, the Schwarz, inequality, and the many extensions of Parseval's equality. Hence, this method answers the above question as a special case and extends to functions of more than one variable and other types of integral trans forms that may interest the systems analysts.

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