Open AccessSome inequalities of Glaeser-Bronšteĭn type
Author(s) -
Sergio Spagnolo,
Giovanni Taglialatela
Publication year - 2006
Publication title -
atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.824
H-Index - 28
eISSN - 1720-0768
pISSN - 1120-6330
DOI - 10.4171/rlm/474
Subject(s) - mathematics , pointwise , lipschitz continuity , type (biology) , polynomial , homogeneous , pure mathematics , order (exchange) , inequality , combinatorics , homogeneous polynomial , mathematical analysis , ecology , finance , matrix polynomial , economics , biology
The classical Glaeser estimate is a special case of the Lemma of Bronshtein which states the Lipschitz continuity of the roots of a hyperbolic polynomial whose coefficients depend on a real parameter.\ud\udHere we prove a pointwise estimate for the successive derivatives of the coefficients of the polynomial in term of certain nonnegative functions which are symmetric polynomials of the roots (hence also of the coefficients). These inequalities are very helpful in the study of the Cauchy problem for homogeneous weakly hyperbolic equations of higher order