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Harmonic synthesis for subgroups

Carl S. Herz (1973)

Annales de l'institut Fourier

Let G be a locally compact group and H a closed subgroup. Then H is always a set of local spectral synthesis with respect to the algebra A p ( G ) , where A 2 ( G ) is the Fourier algebra in the sense of Eymard. Global synthesis holds if and only if a certain condition (C) is satisfied; it is whenever the subgroup H is amenable or normal. Global synthesis implies that each convolution operator on L p ( G ) with support in H which is the ultraweak limit of measures carried by H . The problem of passing from local to global...

Harmonic synthesis of solutions of elliptic equation with periodic coefficients

Victor P. Palamodov (1993)

Annales de l'institut Fourier

An elliptic system in ℝ n , which is invariant under the action of the group ℤ n is considered. We construct a holomorphic family of finite-dimensional subrepresentations of the group in the space of solutions (Floquet solutions), such that any solution of the growth O ( exp ( a | x | ) ) at infinity can be rewritten in the form of an integral over the family.

Henkin measures, Riesz products and singular sets

Evgueni Doubtsov (1998)

Annales de l'institut Fourier

The mutual singularity problem for measures with restrictions on the spectrum is studied. The d -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.

High order representation formulas and embedding theorems on stratified groups and generalizations

Guozhen Lu, Richard Wheeden (2000)

Studia Mathematica

We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable L 1 to L 1 Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and L 1 to L 1 Poincaré...

Hilbert C*-modules from group actions: beyond the finite orbits case

Michael Frank, Vladimir Manuilov, Evgenij Troitsky (2010)

Studia Mathematica

Continuous actions of topological groups on compact Hausdorff spaces X are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging allows one to derive a C*-valued inner product and a Hilbert C*-module which serve as an environment to describe characteristics of the group action. For Lyapunov stable actions the derived invariant mean M ( ϕ x ) is continuous on X for any ϕ ∈ C(X), and the induced C*-valued...

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