Uniform pointwise bounds for matrix coefficients of unitary representations on semidirect products

Higher Order Correlations for Group Actions

“…More general results giving quantitative bounds for representations of semidirect products have been established by Oh [70] and Wang [87].…”

Effective decay of multiple correlations in semidirect product actions

“…Our method was inspired by a proof of quantitative decay of matrix coefficients given in [9]. Initially we had worked out the case SL(n, R) only, when the paper of Zhenqi Jenny Wang [23] was brought to our attention which generalized computations in [9]; this led us to expand the setting and try to isolate parts of the computation that can work in more general settings. Apart from methods, we have adopted notation from these expositions, so the reader is advised to consult them for further reference.…”

“…Note that these are K -subgroups of the K -group Z . We then have the following decomposition (see [4] and the discussion in [23]):…”

“…Since the precise statement of our result is too technical to give in the introduction, we will give a simplified description here and refer to Section 4 for the full version. This paper relies heavily on the work of Wang in [23]. References to proofs in [23] abound but an attempt has been made to isolate the parts of [23] most useful to us and present them as standalone lemmas.…”

“…This paper relies heavily on the work of Wang in [23]. References to proofs in [23] abound but an attempt has been made to isolate the parts of [23] most useful to us and present them as standalone lemmas. Whenever we make use of a result or method of [23], we will mention it explicitly and give specific reference within that work.…”