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Article

On Mutually Inverse Transforms of Functions on a Half-Line

Doklady Mathematics. 2019. Vol. 100. No. 3. P. 1-4.
Protasov V. Y., Shirokov M.

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 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.