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math.FA2023
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig, Irina Shafkulovska
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a…
math.CA2023
A note on energy minimization in dimension 2
Markus Faulhuber, Irina Shafkulovska, Ilia Zlotnikov
Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural…