Premium
Approximate Monotonicity: Theory and Applications
Author(s) -
Elsken T.,
Pearson D. B.,
Robinson P. M.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/53.3.489
Subject(s) - monotonic function , mathematical economics , mathematics , calculus (dental) , computer science , mathematical analysis , medicine , dentistry
The ideas of value distribution for measurable functions from R to R are applied to functions which are approximately monotonic on sets of positive measure. (For definitions see §1.) A function p ( x ) is introduced, describing the local relative value distribution in the neighbourhood of a point x , and it is shown that almost everywhere p ( x ) = 0 or 1 2 wherever p ( x ) exists, implying approximate differentiability, with the function approximately oscillatory elsewhere. These results are applied to the analysis of angular boundary behaviour for Herglotz functions, where they have implications for the spectral analysis of differential and other operators.