arXiv subjects

Jordy Timo van Velthoven

Publications and source records attributed to Jordy Timo van Velthoven.

38 records · Page 3Linked to original sources

arXiv2019

Criteria for generalized translation-invariant frames

This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower frame bound. Contrary to known conditions of a similar nature, the estimates take the phase of the generating functions in consideration and not only their modulus. The possibility of phase cancellations makes these estimates optimal for tight frames. The results on generalized translation-invariant systems will be proved in the setting of locally compact abelian groups, but even for euclidean space and the special case of (composite) wavelet systems the results are new.

math.FA↗

arXiv2019

On the local integrability condition for generalised translation-invariant systems

This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calderón integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions for satisfying the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system.

math.FA↗