2015/10/07 by Führ, Hartmut, Maus, Yannic
#42C40 #94A20 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1510.01832
A bounded, Riemann integrable and measurable set K⊂ ℝd, which fulfills ∑γ∈Γ\mathbb1K(x-γ)=k almost everywhere, x∈ℝd for a lattice Γ⊂ℝd is called k-tiling. If K⊂ℝd is k-tiling L2(K) will admit a Riesz basis of exponentials. We use this result to construct generalized Riesz wavelet bases of L2(ℝ2), arising from the action of suitable subsets of the affine group. One example of our construction is the first known shearlet Riesz basis.