On mutually inverse transforms of functions on a half-line
Classical Analysis and ODEs
2021-05-21 v1 Mathematical Physics
Functional Analysis
Metric Geometry
math.MP
Optimization and Control
Abstract
Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every nonnegative function. In particular, this composition is the identity transform on the class of nonnegative concave functions. Applications of this result to some problems of mathematical physics are indicated. Several open questions are formulated.
Cite
@article{arxiv.2105.09709,
title = {On mutually inverse transforms of functions on a half-line},
author = {V. Yu. Protasov and M. E. Shirokov},
journal= {arXiv preprint arXiv:2105.09709},
year = {2021}
}
Comments
7 pages, any comments are welcome