Approximate monotonicity: Theory and applications

Autor(en): Elsken, T
Pearson, DB
Robinson, PM
Stichwörter: Mathematics; OPERATORS
Erscheinungsdatum: 1996
Herausgeber: LONDON MATH SOC
Journal: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volumen: 53
Ausgabe: 3
Startseite: 489
Seitenende: 502
Zusammenfassung: 
The ideas of value distribution for measurable functions from pg 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 differentiabiilty, 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.
ISSN: 00246107
DOI: 10.1112/jlms/53.3.489

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