{"product_id":"weighted-approximation-with-varying-weight-9783540577058","title":"Weighted Approximation with Varying Weight","description":"\u003cp\u003e • Author(s): Vilmos Totik\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eA new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w\"n\"(\" \"= uppercase)P\"n\"(\" \"= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45280383402135,"sku":"9783540577058","price":1814.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783540577058.webp?v=1769296170","url":"https:\/\/atlanticbooks.com\/products\/weighted-approximation-with-varying-weight-9783540577058","provider":"Atlantic Books","version":"1.0","type":"link"}