On the decomposition of L-2(Gamma\G) in the cocompact case (CROSBI ID 152413)
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Muić, Goran
engleski
On the decomposition of L-2(Gamma\G) in the cocompact case
Let \Gamma be a discrete cocompact subgroup of a semisiple real group G. By a well-known theorem of Gelfand– Graev– Piatetski Shapiro, the right– regular representation L2(\Gamma\G) decomposes into a direct sum of irreducible unitary representations of G, each appearing with a finite multiplicity. Understanding of the spectral decomposition of L2(\Gamma\G) is very important and was studied by a number of authors. In spite of those efforts, the decomposition of L2(\Gamma\G) is still rather mysterious. In the paper the author proves new results in the direction of understanding spectral decomposition of L2(\Gamma\G). New method applied in the paper is use of types of compact subgroups, and relating them to members of the spectral decomposition of L2(\Gamma\G).
semisimple real groups; lattices; automorphic forms; spectral decomposition
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