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Information × Registration Number 0221U105804, 0121U111273 , R & D reports Title Operators in infinite-dimensional spaces: the interplay between geometry, algebra and topology popup.stage_title Head Kadets Volodymyr M., Доктор фізико-математичних наук Registration Date 02-09-2021 Organization V.N. Karazin Kharkiv National University popup.description2  Research objects are Banach spaces, linear operators in Banach spaces, entire functions and spaces of entire functions, linear operators that decrease the number of nonreal roots of polynomials and entire functions, implicit linear nonhomogeneous difference equations over a non-Archimedean ring, polynomial solutions of linear difference and differential equations, the solvability set of a linear nonhomogeneous difference equation. The Purpose of work is to study the most urgent scientific questions, the progress in which is necessary for the completeness of the theory that is planned to be built in the monograph; to develop further the analytic technique that the authors possess, and to apply it to the problems considered in the Project. Research methods consist in application of the properties of corresponding spaces, renormings, filters and ultraproducts, a play with slices and extreme points. Results: we study conditions for stability of the alternative Daugavet property with respect to ultraproducts; implicit linear nonhomogeneous difference equation; linear operators that preserve hyperbolicity; geometry of the unit sphere of a Banach algebra, and integrability of Banach space-valued multifunctions. We have written a part of the text of the future monograph about the Daugavet equation and its generalizations. We published 5 research papers, one of them in a journal of the first quartile, two in journals of the second quartile, and one in a journal of the third quartile. Product Description popup.authors Selutin Dmitro D. Vushnykova Anna M. HEFTER SERHII L. Goncharyk Anna B. ZAVARZINA OLESIA OLEHIVNA Kadets Volodimir M. Lotarezs Lyana A. Nguen Hien T Shevchenko Olga Sergiivna popup.nrat_date 2021-09-02 Close