Geodesic
Compound cubature formulas on a lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 59-74

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In the present paper lattice optimal cubature formulas are constructed by the variational method in the Sobolev space. In addition, the square of the norm of the error functional of the constructed lattice optimal cubature formulas in the conjugate Sobolev space is explicitly calculated.
Keywords: Sobolev space, extremal function, composite lattice optimal cubature formulas, error functional. 
@article{IVM_2023_11_a4,
     author = {Kh. M. Shadimetov and N. H. Mamatova},
     title = {Compound cubature formulas on a lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {59--74},
     publisher = {mathdoc},
     number = {11},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_11_a4/}
}
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Kh. M. Shadimetov; N. H. Mamatova. Compound cubature formulas on a lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 59-74. http://geodesic.mathdoc.fr/item/IVM_2023_11_a4/