Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.

Título inglés	Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.
Título español	Algebras de Clifford, transformadas de Fourier y operadores de convolución singulares sobre superficies de Lipschitz.
Autor/es	Li, Chun ; McIntosh, Alan ; Qian, Tao
Organización	Sch. Math. Phys. Comput. Electron. Macquarie Univ., Port Macquarie (New South Wales), Australia;Dep. Math. Univ. New England, Armidale (New South Wales), Australia
Revista	0213-2230
Publicación	1994, 10 (3): 665-721, 16 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In the Fourier theory of functions of one variable, it is common to extend a function and its Fourier transform holomorphically to domains in the complex plane C, and to use the power of complex function theory. This depends on first extending the exponential function eixξ of the real variables x and ξ to a function eizζ which depends holomorphically on both the complex variables z and ζ . Our thesis is this. The natural analog in higher dimensions is to extend a function of m real variables monogenically to a function of m+1 real variables (with values in a complex Clifford algebra), and to extend its Fourier transform holomorphically to a function of m complex variables. This depends on first extending the exponential function ei(x,ξ) of the real variables x Î Rm and ξ Î Rm to a function e(x,ζ) which depends monogenically on x = x + xLeL Î Rm+1 and holomorphically on ζ = ξ + iη Î Cm.
Clasificación UNESCO	120211
Palabras clave español	Algebras de Clifford ; Transformada de Fourier ; Dominios de Lipschitz ; Convolución ; Funciones de variable compleja
Código MathReviews	MR1308706
Código Z-Math	Zbl 0817.42008
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