Journal of Lie Theory

no. 2
A Plancherel Formula for Representative Functions on Semisimple Lie Groups
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 493-505
A Plancherel formula is given for representative functions on a connected semisimple Lie group G. Since the matrix coefficients for the irreducible finite-dimensional representations are not necessarily square-integrable, an alternative to the Schur Orthogonality Relations is given using invariant differential operators. The corresponding operator analysis is summarized.
DOI: 10.5802/jolt.735
Classification: 22E46
Keywords: Semisimple Lie group, Schur orthogonality relations, matrix coefficient, representative function, Plancherel formula 
@article{JOLT_2013_23_2_a7,
     author = {R. W. Donley and Jr.},
     title = {A {Plancherel} {Formula} for {Representative} {Functions} on {Semisimple} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {493--505},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.735},
     zbl = {1277.22012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.735/}
}
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R. W. Donley; Jr. A Plancherel Formula for Representative Functions on Semisimple Lie Groups. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 493-505. doi: 10.5802/jolt.735

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