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The convolution structure for Jacobi function expansions

Mogens Flensted-Jensen Matematisk Institut, Universitetparken 5, Copenhagen, Denmark Tom Koornwinder Matematisk Institut, Universitetparken 5, Copenhagen, Denmark

TBD mathscidoc:1701.332386

Arkiv for Matematik, 11, (1), 245-262, 1973.2
The product ϕ_{λ}^{(α,β)}(t_{1})ϕ_{λ}^{(α,β)}(t_{2}) of two Jacobi functions is expressed as an integral in terms of ϕ_{λ}^{(α,β)}(t_{3}) with explicit non-negative kernel, when α≧β≧−1/2. The resulting convolution structure for Jacobi function expansions is studied. For special values of α and β the results are known from the theory of symmetric spaces.
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@inproceedings{mogens1973the,
  title={The convolution structure for Jacobi function expansions},
  author={Mogens Flensted-Jensen, and Tom Koornwinder},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203452331369195},
  booktitle={Arkiv for Matematik},
  volume={11},
  number={1},
  pages={245-262},
  year={1973},
}
Mogens Flensted-Jensen, and Tom Koornwinder. The convolution structure for Jacobi function expansions. 1973. Vol. 11. In Arkiv for Matematik. pp.245-262. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203452331369195.
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