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	Generalized Helgason-Fourier Transforms Associated to Variants of the Laplace-Beltrami Operators on the Unit Ball in R-n
	Liu, Congwen ; Peng, Lizhong
	2009
关键词	generalized Helgason-Fourier transforms inversion formula Weinstein operator real hyperbolic space Poisson transform Plancherel theorem heat kernel HYPERBOLIC SPACE EXCEPTIONAL SETS HEAT KERNEL POTENTIALS
英文摘要	In this paper we develop a harmonic analysis associated to the differential operators Delta(theta) := 1-vertical bar x vertical bar(2)/4{(1 - vertical bar x vertical bar(2)) Sigma(n)(j=1) partial derivative(2)/partial derivative x(j)(2) -2 theta Sigma(n)(j=1) x(j) partial derivative/partial derivative x(j) + theta(2 - n - theta)} in a parallel way to that on real hyperbolic space. We make a detailed study of the generalized Helgason-Fourier transform and the theta-spherical transform associated to these differential operators. In particular, we obtain the inversion formula and the Plancherel theorem for them. As an application, we solve the relevant heat equation.; Mathematics; SCI(E); 1; ARTICLE; 3; 1457-1491; 58
语种	英语
出处	SCI
出版者	indiana university mathematics journal
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/396783]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, Congwen,Peng, Lizhong. Generalized Helgason-Fourier Transforms Associated to Variants of the Laplace-Beltrami Operators on the Unit Ball in R-n. 2009-01-01.

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