@inbook{2f83c1fbd43944dba0367ff1abaa9540,

title = "An operator equation generalizing the leibniz rule for the second derivative",

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.",

author = "Hermann K{\"o}nig and Vitali Milman",

note = "Funding Information: Supported in part by the Alexander von Humboldt Foundation by ISF grant 387/09 BSF grant 2006079. ",

year = "2012",

doi = "10.1007/978-3-642-29849-3_16",

language = "אנגלית",

isbn = "9783642298486",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "279--299",

booktitle = "Geometric Aspects of Functional Analysis",

}