t-design curves and mobile sampling on the sphere

31.03.2023 09:45 - 11:15

Karlheinz Gröchenig and Martin Ehler (University of Vienna)

Line integrals along t-design curves yield exact quadrature rules for polynomials of degree t on the d-sphere, whereas the classical t-designs use point evaluations for quadrature. We will show that on the 2-sphere in R3 t-design curves of the optimal length O(t) exist, and perhaps indicate the existence of t-design curves for higher-dimensional spheres. 



K. Gröchenig, L. Liehr, J. L. Romero and I. Shafkulovska
SR11 (second floor)