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Let G be a second countable, locally compact group and let f be a continuousHerz-Schur multiplier on G. Our main result gives the existence of a (notnecessarily uniformly bounded) strongly continuous representation on a Hilbertspace, such that f is the coefficient of this representation with respect totwo vectors with bounded orbit. Moreover, we show that the norm of therepresentation of an element g from G is at most exponential in terms of themetric distance from g to the identity element of G.

Herz-Schur Multipliers and Non-Uniformly Bounded Representations of Locally Compact Groups