Schoenberg Representations and Gramian Matrices of Matérn Functions
  We represent Matérn functions in terms of Schoenberg's integrals which
ensure the positive definiteness and prove the systems of translates of
Matérn functions form Riesz sequences in $L^2(\R^n)$ or Sobolev spaces. Our
approach is based on a new class of integral transforms that generalize Fourier
transforms for radial functions. We also consider inverse multi-quadrics and
obtain similar results.
