Landau and Kolmogoroff type polynomial inequalities
Carregando...
Fonte externa
Fonte externa
Data
Autores
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Gordon Breach Sci Publ Ltd
Tipo
Artigo
Direito de acesso
Acesso aberto
Fonte externa
Fonte externa
Resumo
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.
Descrição
Palavras-chave
Landau and Kolmogoroff type inequalities, Markov's inequality, hermite polynomials, extremal polynomials, Rayleigh-Ritz theorem
Idioma
Inglês
Citação
Journal of Inequalities and Applications. Reading: Gordon Breach Sci Publ Ltd, v. 4, n. 4, p. 327-338, 1999.
