Harmonic Analysis in Euclidean Space
The ideas that led to the representation of periodic functions as trigonometric series will be applied to functions defined on Rn. As before, we will attempt to expand functions in terms of characters parameterized, however, by Rn instead of Z. As a consequence, series expansions will be replaced by integral expansions, and the theory of inversion will have a different flavor than in the previous case. However, the underlying themes in this chapter will be the same as those of chapter 2: convolution and approximation, Plancherel’s theorem, Bochner’s theorem etc.
KeywordsAssure Peri Convolution Lution Nite
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