Advanced Mathematics, Computations and Applications 2015

October 19-23, 2015, Akademgorodok, Novosibirsk, Russia

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Стрелков Н.  

Wavelets, optimal cubature formulas and densest lattice packing

WAVELETS, OPTIMAL CUBATURE FORMULAS AND DENSEST LATTICE PACKING

N. A. Strelkov
Yaroslavl state university, Yaroslavl
strelkov@uniyar.ac.ru

Two approaches to the construction of optimal cubature formulae are considered. The approximation subspace is the span of lattice translations of the fixed function. This problem is closely associated with the finding of characteristics of the best projection-net approximations. For example in some cases the optimal lattice satisfies the following condition: the dual lattice generates the densest packing of Lebesgue sets of some function depending on the norm of Hormander spaces (for Sobolev spaces the problem comes to the densest lattice packing of spheres).