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  1. ; (, Journal of Lie Theory)
    Abstract. Let š˜Ž be a real semisimple algebraic Lie group and š˜ a real reductive algebraic subgroup. We describe the pairs (š˜Ž,š˜) for which the representation of š˜Ž in LĀ²(š˜Ž/š˜) is tempered. The proof gives the complete list of pairs (š˜Ž,š˜) for which LĀ²(š˜Ž/š˜) is not tempered. When š˜Ž and š˜ are complex Lie groups, the temperedness condition is characterized by the fact that š˜µš˜©š˜¦ š˜“š˜µš˜¢š˜£š˜Ŗš˜­š˜Ŗš˜»š˜¦š˜³ š˜Ŗš˜Æ š˜ š˜°š˜§ š˜¢ š˜Øš˜¦š˜Æš˜¦š˜³š˜Ŗš˜¤ š˜±š˜°š˜Ŗš˜Æš˜µ š˜°š˜Æ š˜Ž/š˜ š˜Ŗš˜“ š˜·š˜Ŗš˜³š˜µš˜¶š˜¢š˜­š˜­š˜ŗ š˜¢š˜£š˜¦š˜­š˜Ŗš˜¢š˜Æ. š˜”š˜¢š˜µš˜©š˜¦š˜®š˜¢š˜µš˜Ŗš˜¤š˜“ š˜šš˜¶š˜£š˜«š˜¦š˜¤š˜µ š˜Šš˜­š˜¢š˜“š˜“š˜Ŗš˜§š˜Ŗš˜¤š˜¢š˜µš˜Ŗš˜°š˜Æ: Primary 22š„46; secondary 43š€85, 22š…30. š˜’š˜¦š˜ŗ š˜žš˜°š˜³š˜„š˜“: Lie groups, homogeneous spaces, tempered representations, unitary representations, matrix coefficients, symmetric spaces. 
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