This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Quite recently, a first approach has been derived in [4]. We present an alternative version which deviates from [4] mainly by a different generalization of the shear component. It turns out that the resulting integral transform is again associated with a square-integrable group representation.

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many) L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant...

For any natural number n, the group $$G_n$$ of all invertible affine transformations n-dimensional Euclidean space has, up to equivalence, just one square-integrable representation and left regular is a multiple this representation. We provide concrete realization $$\sigma $$ distinguished in two-dimensional case. explicitly decompose Hilbert $$L^2(G_2)$$ as direct sum left-invariant closed sub...

Suppose that G is a Lie group. which for the purpose of this introduction, we take to be a real form of a simply connected complex semisimple group. Suppose that square integrable representations for G exist and that f is a matrix coefficient of a square integrable representation belonging to the unitary equivalence class co. Harish-Chandra has shown how to evaluate the integral off with respec...

The minimal representation π of O(p, q) (p + q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of Rp+q−2. This model presents a close resemblance of the Schrödinger model of the Segal-Shale-Weil representation of the metaplectic group. We shall give explicit integral formulas for the ‘inversion’ together with the analytic continuation to a certai...