
Accession Number : AD0755432
Title : Complete Orthonormal Set of TwoDimensional HaarLike Functions.
Descriptive Note : Interim rept.,
Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C
Personal Author(s) : Shore,John E.
Report Date : 10 JAN 1973
Pagination or Media Count : 27
Abstract : A set of twodimensional functions is defined. Expansions of two dimensional functions f(x, y) in terms of this set have convergence properties analogous to those of onedimensional Haar series. The Nth partial sum (P sub N)(x, y) is a step function of 2 sup (2N) square steps each of area 1/2 sup (2N). The value of (P sub N)(x, y) on any step is the mean value of f(x, y) over the area covered by the step. If f(x, y) is continuous or has a finite number of discontinuities along binaryrational line segments, then (P sub N)(x, y) converges uniformly. If f(x, y) has a finite number of discontinuities along binaryirrational line segments, then (P sub N))x, y) converges pointwise, except along the discontinuities. Accuracy of the estimate (P sub N) and the convergence rate are analogous to those for onedimensional Haar series. (Author)
Descriptors : (*FUNCTIONS(MATHEMATICS), THEOREMS), SERIES(MATHEMATICS), CONVERGENCE, FOURIER ANALYSIS, BINARY ARITHMETIC, CODING, PATTERN RECOGNITION, TRANSFORMATIONS(MATHEMATICS)
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE