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

Chun Li; Alan McIntosh; Tao Qian

Revista Matemática Iberoamericana (1994)

- Volume: 10, Issue: 3, page 665-721
- ISSN: 0213-2230

## Access Full Article

top## Abstract

top## How to cite

topLi, Chun, McIntosh, Alan, and Qian, Tao. "Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.." Revista Matemática Iberoamericana 10.3 (1994): 665-721. <http://eudml.org/doc/39468>.

@article{Li1994,

abstract = {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 ∈ Rm and ξ ∈ Rm to a function e(x,ζ) which depends monogenically on x = x + xLeL ∈ Rm+1 and holomorphically on ζ = ξ + iη ∈ Cm.},

author = {Li, Chun, McIntosh, Alan, Qian, Tao},

journal = {Revista Matemática Iberoamericana},

keywords = {Algebras de Clifford; Transformada de Fourier; Dominios de Lipschitz; Convolución; Funciones de variable compleja; Lipschitz surfaces; Clifford algebra; Fourier transform; singular convolution operators},

language = {eng},

number = {3},

pages = {665-721},

title = {Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.},

url = {http://eudml.org/doc/39468},

volume = {10},

year = {1994},

}

TY - JOUR

AU - Li, Chun

AU - McIntosh, Alan

AU - Qian, Tao

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

JO - Revista Matemática Iberoamericana

PY - 1994

VL - 10

IS - 3

SP - 665

EP - 721

AB - 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 ∈ Rm and ξ ∈ Rm to a function e(x,ζ) which depends monogenically on x = x + xLeL ∈ Rm+1 and holomorphically on ζ = ξ + iη ∈ Cm.

LA - eng

KW - Algebras de Clifford; Transformada de Fourier; Dominios de Lipschitz; Convolución; Funciones de variable compleja; Lipschitz surfaces; Clifford algebra; Fourier transform; singular convolution operators

UR - http://eudml.org/doc/39468

ER -

## Citations in EuDML Documents

top- Garth Gaudry, Tao Qian, Silei Wang, Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves
- Brian Jefferies, Alan McIntosh, James Picton-Warlow, The monogenic functional calculus
- Tao Qian, Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.