Published paper

Asymptotic properties of unitary representations

Roger E. Howe, Calvin C. Moore

Publication metadata

Journal citation: Journal of Functional Analysis 32(1), 72–96 (1979)
Publication date: 1979
DOI: 10.1016/0022-1236(79)90078-8 ↗

Abstract

The Howe–Moore vanishing theorem rules out the nontrivial endpoint at $z=1$ in the rank-one proof that spectral gap gives a finite temperedness exponent.

Role in dependence graphs

Proof-critical source

Bounded trajectories of quasi-rays

This paper is included only for the following marked statement:

Howe–Moore vanishing theorem · source pp. 72–96; EMV Appendix C, pp. 80–81Forces nontrivial matrix coefficients to vanish at infinity and rules out a nontrivial complementary-series endpoint at $z=1$ .

Proof-critical source

Submanifold-genericity of $\mathbb{R}^d$-actions and uniform multiplicative Diophantine approximation

This paper is included only for the following marked statement:

Howe–Moore vanishing theorem · source pp. 72–96; EMV Appendix CRules out a nontrivial endpoint at z=1.

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