Geodesic
A Plancherel Formula for Representative Functions on Semisimple Lie Groups
Journal of Lie theory, Tome 23 (2013) no. 2, pp. 493-505

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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.
Classification : 22E46
Mots-clés : Semisimple Lie group, Schur orthogonality relations, matrix coefficient, representative function, Plancherel formula 
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     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},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a7/}
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R. W. Donley; Jr. . A Plancherel Formula for Representative Functions on Semisimple Lie Groups. Journal of Lie theory, Tome 23 (2013) no. 2, pp. 493-505. http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a7/