@article{95537f5547124ef5935df4b42de0d7db,

title = "The extended leibniz rule and related equations in the space of rapidly decreasing functions",

abstract = " We solve the extended Leibniz rule T (f · g) = T f · Ag + Af · T g for operators T and A in the space of rapidly decreasing functions in both cases of complex and real-valued functions. We find that T f may be a linear combination of logarithmic derivatives of f and its complex conjugate f with smooth coefficients up to some finite orders m and n respectively and Af = f m · f n . In other cases T f and Af may include separately the real and the imaginary part of f. In some way the equation yields a joint characterization of the derivative and the Fourier transform of f. We discuss conditions when T is the derivative and A is the identity. We also consider differentiable solutions of related functional equations reminiscent of those for the sine and cosine functions.",

keywords = "Extended Leibniz rule, Fourier transform, Rapidly decreasing functions",

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

note = "Publisher Copyright: {\textcopyright} Hermann K{\"o}nig and Vitali Milman, 2018.",

year = "2018",

doi = "10.15407/MAG14.03.336",

language = "אנגלית",

volume = "14",

pages = "336--361",

journal = "Journal of Mathematical Physics, Analysis, Geometry",

issn = "1812-9471",

publisher = "ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering",

number = "3",

}