Accession Number : AD0690329

Title :   ON THE APPROXIMATION OF CONTINUOUS FUNCTIONS OF TWO VARIABLES BY ALGEBRAIC POLYNOMIALS,

Descriptive Note : APL Library bulletin translation series,

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

Personal Author(s) : Malozemov,V. N.

Report Date : 09 MAY 1969

Pagination or Media Count : 25

Abstract : The following theorem of S. A. Telyakovskii is generalized in the present paper for the two-dimensional case: for every function f(x) continuous on the segment (-1,1) and for any positive n one can construct an algebraic polynomial g sub n(f;x) of degree not higher than n such that for all x epsilon (-1,1) the inequality the absolute value of (f(x)-(g sub n)(f;x)) = or < (A sub1) omega (f;(the square root of (1-x squared))/n) is fulfilled, where A sub 1 is an absolute constant and omega (f) is the continuity modulus of the function f. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), APPROXIMATION(MATHEMATICS)), (*APPROXIMATION(MATHEMATICS), *POLYNOMIALS), INTERPOLATION, INEQUALITIES, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE