Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: on the one hand, Lp estimates, which are a dual formulation of the Kunze-Stein phenomenon, and which hold for all matrix coef-ficients, and on the other pointwise estimates related to asymptotic expansions at infinity, which are more precise but only hold for a restricted class of matrix coefficients. In this paper we prove a new type of estimate for the irreducibile unitary representations of SL(2, R) and for the so-called meta-plectic representation, which we believe has the best features of, and implies, both forms of estimate described above. As an application outside representation theory, we prove a new L2 estimate of dispersive type for the free Schro center dot dinger equation in Rn.

ESTIMATES FOR MATRIX COEFFICIENTS OF REPRESENTATIONS

Bruno, T;Cowling, MG;
2022-01-01

Abstract

Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: on the one hand, Lp estimates, which are a dual formulation of the Kunze-Stein phenomenon, and which hold for all matrix coef-ficients, and on the other pointwise estimates related to asymptotic expansions at infinity, which are more precise but only hold for a restricted class of matrix coefficients. In this paper we prove a new type of estimate for the irreducibile unitary representations of SL(2, R) and for the so-called meta-plectic representation, which we believe has the best features of, and implies, both forms of estimate described above. As an application outside representation theory, we prove a new L2 estimate of dispersive type for the free Schro center dot dinger equation in Rn.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1097073
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