Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Herz-Schur multipliers and non-uniformly bounded representations of locally compact groups

Steenstrup T.

Probability and Mathematical Statistics

2013

Vol. 33, Fasc. 2

213--223

Let G be a second countable, locally compact group and let φ be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation π of G on a Hilbert space ℋ , together with vectors ξ, η ϵ ℋ, such that φ(y−1x) = ⟨π(x)ξ, π(y−1) * η⟩ for x, y ϵ G and supx ϵ G ∥π(x)ξ supy ϵ G ∥π(y−1) * η∥ = ∥φ∥ M0A(G). Moreover, we obtain control over the growth of the representation in the sense that ∥π(g)∥≤ exp ( c/2 d(g, e)) for g ϵ G, where e ϵ G is the identity element, c is a constant, and d is a metric on G.