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Registration Number

0225U002127, (0120U100195) , R & D reports

Title

Operator theory and functional analysis in modern mathematics and applications

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Теорія операторів та функціональний аналіз у сучасній математиці та застосуваннях

Head

Ostrovskyi Vasyl L., д.ф.-м.н.

Registration Date

19-02-2025

Organization

Institute of Mathematics of the National Academy of Sciences of Ukraine

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The purpose of the work is to develop important and relevant sections of functional analysis, in particular, the spectral theory of operators and the theorey of representations of involutional algebras, which can be used to study relevant models of modern mathematical physics, quantum information, and other applications.

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 Research report: 94 pages, 3 chapters, 96 sources. Key words: WICK CALCULUS, GLOBAL DIMENSION, QUANTUM DESIGN, QUANTUM CHANNEL, COLLECTION OF ISOMETRIES, NONLOCAL POTENTIAL, INVERSE SCATTERING PROBLEM, PSEUDOCOMPACT ALGEBRA, EXTENDED STOCHASTIC INTEGRAL, SYSTEM OF SUBSPACES, SUM OF ORTHOPROJECTIONS, SUM OF SUBSPACES, TRIANGULAR GROUP. The objects of research are nonlinear equations of mathematical physics, sets of subspaces of Hilbert or Banach spaces, operator algebras and their images, Wick calculus in non-Gaussian analysis. The purpose of the work is to develop important and relevant sections of functional analysis, in particular, the spectral theory of operators and the theorey of representations of involutional algebras, which can be used to study relevant models of modern mathematical physics, quantum information, and other applications. In the work, the methods of spectral theory of operators, theory of nonlinear equations, theory of representations of operator algebras, stochastic analysis were used. New results were obtained in functional analysis and its applications, in particular, regarding direct and inverse problems of the theory of nonlinear equations, mathematical problems of quantum information, the structure and properties of collections of subspaces of Hilbert and Banach spaces, representations of operator algebras, problems of infinite-dimensional analysis that arise in stochastic analysis. The results of the research can be used in further research on the topic of the project, as well as in the study of models of mathematical physics, frame theory, quantum information theory, projection methods, etc.

Product Description

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Kaliuzhnyi Oleksandr O.
Kachanovskyi Mykola O.
Nyzhnyk Leonid P.
Ostrovskyi Vasyl L.
Popova Nataliia D.
Rabanovych Viacheslav I.
Samoilenko Yurii S.
Strilets Oleksandr V.
Feshchenko Ivan S.
Yusenko Kostiantyn A.
Yakymenko Danylo Yu.

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2025-02-19