
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 twodimensional 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 (1x 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