In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the Lp space L2+ε(G) for any ε > 0. == Formulation == This condition, as just given, is slightly weaker than the condition that the matrix coefficients are square-integrable, in other words lie in L2(G), which would be the definition of a discrete series representation.
In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the Lp space L2+ε(G) for any ε > 0. == Formulation == This condition, as just given, is slightly weaker than the condition that the matrix coefficients are square-integrable, in other words lie in L2(G), which would be the definition of a discrete series representation.
Source: Wikipedia "Tempered representation" · CC BY-SA 4.0
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