Accession Number : AD0693363

Title :   ON NORMS OF LINEAR POLYNOMIAL OPERATORS.

Descriptive Note : APL Library bulletin translations series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Telyakovskii,S. A.

Report Date : 15 AUG 1969

Pagination or Media Count : 16

Abstract : Let C denote the space of all continuous periodic functions and let U sub n be a linear operator transforming every f epsilon C into some trigonometrical polynomial of degree n, U sub n (f,x) = 1/2 phi sub zero (f) + Summation, k = 1 to k = n, of the quantity (phi sub k (f) cos kx + psi sub k (f) sin kx), where phi sub k and psi sub k are certain linear functionals given in C and completely determining the operator U sub n. The paper gives an estimate of the norm of the arbitrary operator U sub n.

Descriptors :   (*OPERATORS(MATHEMATICS), *FOURIER ANALYSIS), TRANSFORMATIONS(MATHEMATICS), POLYNOMIALS, INEQUALITIES, SERIES(MATHEMATICS), CONVERGENCE, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE