Open AccessOn mutually inverse transforms of functions on a half-line
Author(s) -
Vladimir Yu. Protasov,
M. E. Shirokov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524895452-455
Subject(s) - mathematics , hilbert space , inverse , real line , composition (language) , class (philosophy) , operator (biology) , pure mathematics , composition operator , line (geometry) , function (biology) , mathematical analysis , space (punctuation) , multiplication operator , computer science , geometry , linguistics , philosophy , biochemistry , chemistry , repressor , artificial intelligence , evolutionary biology , biology , transcription factor , gene , operating system
Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every non-negative function. In particular, this composition is an identical transform on the class of non-negative concave functions. Applications of this result in the operator theory of Hilbert space and in the theory of quantum systems are mentioned. Several open problems are formulated.