"Generalised translations, bandpass bases and splines in higher dimensions"Hogan, JeffreyWe investigate the role of Clifford-analytic techniques in the construction of spline-like functions in higher dimensions and the generation of bandpass bases (consisting of functions whose Fourier transforms are supported on annuli) from bandlimited bases (consisting of functions whose Fourier transforms are supported on balls). The key ingredient is the replacement of the usual translations of harmonic analysis in higher dimensions by generalised translations defined as exponentials of the Dirac operator. |
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