Landau and Kolmogoroff type polynomial inequalities

• Autor(a) principal: Alves, CRR
• Data de Publicação: 1999
• Outros Autores: Dimitrov, D. K.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1155/S1025583499000430; http://hdl.handle.net/11449/21719
• topic: Landau and Kolmogoroff type inequalities; Markov's inequality; hermite polynomials; extremal polynomials; Rayleigh-Ritz theorem

Let 0<j<m less than or equal to n be integers. Denote by parallel to . parallel to the norm parallel to f parallel to(2) = integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.