An operator equation generalizing the leibniz rule for the second derivative

Hermann König, Vitali Milman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We determine all operators and which satisfy the equation 1 This operator equation models the second order Leibniz rule for (f ) with . Under a mild regularity and non-degeneracy assumption on A, we show that the operators T and A have to be of a very restricted type. In addition to the operator solutions S of the Leibniz rule derivation equation corresponding to A = 0, 2 which are of the form T and A may be of the following three types for suitable continuous functions d, c and p and where ε is either 1 or sgnf and p-1. The last operator solution is degenerate in the sense that T is a multiple of A. We also determine all solutions of (1) if T and A operate only on positive-functions or-functions which are nowhere zero.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Pages279-299
Number of pages21
ISBN (Print)9783642298486
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2050
ISSN (Print)0075-8434

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