{"product_id":"chebyshev-splines-and-kolmogorov-inequalities-von-sergey-bagdasarov","title":"Chebyshev Splines and Kolmogorov Inequalities","description":"\u003cp\u003eSince the introduction of the functional classes HW (lI) and WT HW (lI) and their peri­ odic analogs Hw (1I') and ~ (1I'), defined by a concave majorant w of functions and their rth derivatives, many researchers have contributed to the area of ex­ tremal problems and approximation of these classes by algebraic or trigonometric polynomials, splines and other finite dimensional subspaces. In many extremal problems in the Sobolev class W~ (lI) and its periodic ana­ log W~ (1I') an exceptional role belongs to the polynomial perfect splines of degree r, i.e. the functions whose rth derivative takes on the values -1 and 1 on the neighbor­ ing intervals. For example, these functions turn out to be extremal in such problems of approximation theory as the best approximation of classes W~ (lI) and W~ (1I') by finite-dimensional subspaces and the problem of sharp Kolmogorov inequalities for intermediate derivatives of functions from W~. Therefore, no advance in the T exact and complete solution of problems in the nonperiodic classes W HW could be expected without finding analogs of polynomial perfect splines in WT HW .\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783034897815\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783034897815","offer_id":49592320819525,"sku":"9783034897815","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/9ee13474-3ab2-41ba-9bb6-e950b4eae767.jpg?v=1772083185","url":"https:\/\/shop.autorenwelt.de\/en\/products\/chebyshev-splines-and-kolmogorov-inequalities-von-sergey-bagdasarov","provider":"Autorenwelt Shop","version":"1.0","type":"link"}