Email this article On mutually inverse transforms of functions on a half-line
- Authors: Protasov V.Y.1,2, Shirokov M.E.3,4
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Affiliations:
- Lomonosov Moscow State University
- Higher School of Economics
- Steklov Mathematical Institute of Russian Academy of Sciences
- Moscow Institute of Physics and Technology
- Issue: Vol 489, No 5 (2019)
- Pages: 452-455
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18834
- DOI: https://doi.org/10.31857/S0869-56524895452-455
- ID: 18834
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Abstract
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.
About the authors
V. Yu. Protasov
Lomonosov Moscow State University; Higher School of Economics
Author for correspondence.
Email: v-protassov@yandex.ru
Corresponding Member of the Russian Academy of Sciences
Russian Federation, 1, Leninskie gory, Moscow, 119991; 20, Myasnitskaya str., Moscow, 101000M. E. Shirokov
Steklov Mathematical Institute of Russian Academy of Sciences; Moscow Institute of Physics and Technology
Email: msh@mi-ras.ru
Russian Federation, 8, Gubkina street, Moscow, 117966; 9, Institutskiy lane, Dolgoprudny, Moscow region, 141701
References
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- Shirokov M.E. Operator E Norms and Their Use. 2018. arXiv:1806.05668.
- Shirokov M.E., Holevo A.S. Energy-Constrained Diamond Norms and Quantum Dynamical Semigroups // Lobachevskii J. Math. 2019. V. 40. № 10. P. 1569-1586.
- Kato T. Perturbation Theory for Linear Operators. N.Y.; Heidelberg; B.: Springer-Verlag, 1980.
- Simon B. Operator Theory: A Comprehensive Course in Analysis. Pt IV. Amer. Math. Society, 2015.
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