Asymptotic properties of unitary representations Academic Article uri icon

abstract

  • If {variant} is a unitary representation of a locally compact group G, one is very often interested in the asymptotic behavior of the operators {variant}(g) as g tends to in G. Put another way one is interested in what operators not in {variant}(G) can be (weak) limits of the {variant}(g) as g tends to . The first part of the paper deals with the question of what kinds of unitary operators can be limits of {variant}(g), and we show that for connected G the possibilities are very limited. The second part of the paper deals with the question of when one can conclude that essentially the only operator of any kind not in {variant}(G) obtained as a limit of the {variant}(g) is 0. This amounts to showing that the matrix coefficients of {variant} "vanish at ," and we establish affirmative results for irreducible representations of connected algebraic groups over local fields (archimedian and non-archimedian). Such results turn out to have applications to the theory of automorphic forms and to ergodic theory. 1979.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Howe, R. E., & Moore, C. C.

citation count

  • 142

complete list of authors

  • Howe, Roger E||Moore, Calvin C

publication date

  • April 1979