Walsh-Fourier series for functions of n variables with localization

Abstract

AbstractWhen it is desired to represent a function of n variables by a series of the Fourier type, it is customary to construct the relevant complete orthogonal set by taking a set of functions each of which is a product of n functions of single variables. With Walsh functions, an alternative is possible, feasible, and practically implementable. The principal advantage of the alternative scheme is that localization holds in the same sense as for a function of a single variable represented by a series of the Fourier type. Another feature of the alternative method is that the Walsh-Fourier series for certain types of discontinuous functions behave essentially as if those functions were continuous

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