REMEZ-TYPE INEQUALITIES ON THE SIZE OF GENERALIZED POLYNOMIALS Academic Article

abstract

• Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [- 1,1] of algebraic polynomials of degree at most n if the measure of the subset of [-1,1], where the modulus of the polynomial is at most 1, is known. In this paper a numerical version of the Remez inequality is extended for generalized complex algebraic polynomials and its trigonometric and pointwise algebraic analogues are discussed. The results are new even for ordinary polynomials. 1992 Oxford University Press.

authors

• Erdelyi, Tamas

published proceedings

• JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

author list (cited authors)

• ERDELYI, T.

citation count

• 41

complete list of authors

• Erdélyi, Tamás

publication date

• April 1992

publisher

• Wiley  Publisher

published in

• Journal of London Mathematical Society  Journal

keywords

• 10 Reduced Inequalities

Digital Object Identifier (DOI)

• 10.1112/jlms/s2-45.2.255

start page

• 255

end page

• 264

volume

• 45

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1112%2Fjlms%2Fs2-45.2.255

user-defined tag

• 10 Reduced Inequalities