On Mutually Inverse Transforms of Functions on a Half-Line

详细

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 an identity transform in the class of nonnegative concave functions. Applications of this result in Hilbert space operator theory and the theory of quantum systems are indicated. Several open problems are formulated.