The Product Formula for the Spherical Functions on Symmetric Spaces of Noncompact Type

P. Graczyk; P. Sawyer

doi:10.5802/jolt.300

P. Graczyk; P. Sawyer

Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 247-261

Abstract

We prove the existence of the product formula for the spherical functions on symmetric spaces of noncompact type. To this end, we study the analyticity properties of the Cartan decomposition and we find a limited Taylor expansion of the abelian factor in this decomposition.

EuDML Zbl

DOI: 10.5802/jolt.300

Classification: 43A90, 53C35
Keywords: spherical function, symmetric spaces, product formula, kernel function, Abel transform

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     author = {P. Graczyk and P. Sawyer},
     title = {The {Product} {Formula} for the {Spherical} {Functions} on {Symmetric} {Spaces} of {Noncompact} {Type}},
     journal = {Journal of Lie Theory},
     pages = {247--261},
     year = {2003},
     volume = {13},
     number = {1},
     doi = {10.5802/jolt.300},
     zbl = {1023.43005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.300/}
}

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P. Graczyk; P. Sawyer. The Product Formula for the Spherical Functions on Symmetric Spaces of Noncompact Type. Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 247-261. doi: 10.5802/jolt.300

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