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Information × Registration Number 0225U002126, (0120U100169) , R & D reports Title Spectral problems, fractional-differential and non-Archimedean models of modern mathematical physics popup.stage_title Спектральні задачі, дробово-диференціальні та неархімедові моделі сучасної математичної фізики Head Kochubei Anatolii N., Доктор фізико-математичних наук Registration Date 19-02-2025 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The purpose of this work is to develop methods of linear and nonlinear functional analysis, non-Archimedean and fractional calculus and their applications to models of modern mathematical physics and data presentation methods. popup.description2 Research report: 109 p., 6 chapters, 152 sources. Key words: ELLIPTIC EQUATION, PARABOLIC EQUATION, BOUNDARY VALUE PROBLEM, SPECTRUM, NON-ARCHIMEDEAN FIELD, FRACTIONAL CALCULUS, PSEUDO-DIFFERENTIAL OPERATOR, ELLIPTIC BOUNDARY VALUE PROBLEM, GENERALIZED SOBOLEV SPACE, LIZORKIN-TRIBEL SPACE, BESOV SPACE, NOETHER OPERATOR, SPECTRAL EXPANSION, PARABOLIC BOUNDARY VALUE PROBLEM, BOUNDARY VALUE PROBLEM WITH A PARAMETER, OPERATOR INDEX, BOUNDARY THEOREM, STURM-LIOUVILLE OPERATOR. The research object is nonlinear, spectral, fractional-differential and non-Archimedean models of mathematical physics. The purpose of the work is to develop methods of linear and nonlinear functional analysis, non-Archimedean and fractional calculus and their applications to models of modern mathematical physics and data presentation methods. Research methods are modern methods of linear and nonlinear functional analysis and operator theory. Non-Archimedean and discrete fractional calculus have been developed, evolutionary equations of quantum mechanics, elliptic problems with rough boundary conditions, new classes of boundary value problems for a system of ordinary differential equations have been investigated, new conditions for convergence of trigonometric series have been established, and the spectral theory of strongly singular differential operators has been developed. The results are fundamental, meet high-level international standards, make a significant contribution to the development of mathematical science and have prospects for application in related fields. Product Description popup.authors Anop Annа V. Antoniuk Oleksandra V. Artemichenko Zhanna Ya. Atlasiuk Olena M. Herasymenko Viktor I. Horiunov Andrii S. Hrushka Yaroslav I. Kosiak Oleksandr V. Kochubei Anatolii N. Mykhailets Volodymyr A. Molyboha Volodymyr M. Murach Oleksandr O. Serdiuk Mariia V. Soldatov Vitalii O. Chepurukhina Iryna S. popup.nrat_date 2025-02-19 Close