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

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Abstract:

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

Author(s):
Malozemov, V. N.
Author Organization(s):
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
Descriptive Note:
APL Library bulletin translation series,
Supplementary Note:
Trans. of Leningrad Univ. Vestnik (USSR) v23 n19, Seriya Matematiki, Mekhaniki i Astronomii, n4 p73-98 1968, by L. J. Holtschlag.
Annotation:
On the approximation of continuous functions of two variables by Algebraic polynomials--Translation.
Pagination:
0025

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
APL-CLB-3-T-586
Contract/Grant Number(s):
NOw-62-0604
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*FUNCTIONS(MATHEMATICS), APPROXIMATION(MATHEMATICS)), (*APPROXIMATION(MATHEMATICS), *POLYNOMIALS), INTERPOLATION, INEQUALITIES, THEOREMS, USSR
Field(s)/Group(s):
Theoretical Mathematics
Keyword(s):
POLYNOMIAL APPROXIMATIONS, TRANSLATIONS
Report Date:
1969 May 09