{"ID":2864340,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23890","arxiv_id":"2509.23890","title":"Best weighted approximation of some kernels on the real axis","abstract":"We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $\\frac {A+Bt}{(t^2+λ^2)^{s+1}}$, where $A$ and $B$ are fixed complex numbers, $λ\u003e0$, $s\\in {\\mathbb N}$, in the mean square metric.","short_abstract":"We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $\\frac {A+Bt}{(t^2+λ^2)^{s+1}}$, where $A$ and $B$ are fixed complex numbers, $λ\u003e0$, $s\\in {\\mathbb N}$, in the mean square metric.","url_abs":"https://arxiv.org/abs/2509.23890","url_pdf":"https://arxiv.org/pdf/2509.23890v2","authors":"[\"Stanislav Chaichenko\",\"Viktor Savchuk\",\"Andrii Shidlich\"]","published":"2025-09-28T13:52:57Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.CA\",\"math.OC\"]","methods":"[]","has_code":false}