(p, q)-Frame measures on LCA groups: Perturbations and construction

Motivated to generalize the Fourier frame concept Banach spaces we introduce (p, q)-Bessel/frame measures for a given finite measure on LCA groups. We also present general way of constructing measure. Moreover, prove that if has an associated q)-frame measure, then it must have certain uniformity in sense weight is distributed quite uniformly its support. Next, show μ and λ without atoms whose supports form packing pair, μ⁎λ+δg⁎μ does not admit any Finally, analyze stability under small perturbations. new theorems concerning perturbation both Hilbert spaces.