Modern Methods in Operator Theory and Harmonic Analysis

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018.

The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant.

Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

Highlights new results in methods, problems and applications of operator theory and harmonic analysis, presented by leading researchers Touches on recent developments in spectral theory with applications to PDEs and real-world problems Focuses on new trends in operator theory and function spaces theory, such as variable exponent spaces and objects of variable nature

Contenu

Part I: Function Theory and Approximation Theory .- M. L. Goldman and E. Bakhtigareeva: Some General Properties of Operators in Morrey-type Spaces.- V. S. Guliyev, A. Eroglu and G. A. Abasova: Characterization of Parabolic Fractional Maximal Function and its Commutators in Orlicz Spaces.- A. Iosevich and K. Taylor: Finite Trees Inside Thin Subsets of Rd.- A. Karapetyants and J. E. Restrepo: Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Hölder Type Functions.- K.S. Kazarian: Generalized Fourier Series by the Double Trigonometric System.- E. Liflyand: Hardy Type Inequalities in the Category of Hausdorff Operators.- H. R. Malonek, I. Cação, M. I. Falcão and G. Tomaz: Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One.- Y. Sawano: Paraproduct in BesovMorrey Spaces.- Part II: Functional Analysis and Operator Theory .- E. I. Berezhno: Analogs of the Khintchin Kolmogorov Inequalities in Discrete Morrey Spaces.- R. Duduchava: Mellin Convolution Equations.- D. Hasanyan, A. Kamalyan, M. Karakhanyan & I. M. Spitkovsky: Integral Operators of the L-convolution Type in the Case of a Reflectionless Potential.- Y. Krasnov: Spectral Theory for Nonlinear Operators: Quadratic Case.- A. G. Kusraev and Z. A. Kusraeva: Factorization of Order Bounded Disjointness Preserving Multilinear Operators.- D. B. Rokhlin: Robbins-Monro Conditions for Persistent Exploration Learning Strategies.- E. Shulman: On Widths of Invariant Sets.- I. G. Tsar'kov: The Distance Function and Boundedness of Diameters of the Nearest Elements.- Part III: Differential Equations and Mathematical Physics .- H. S. Aslan and M. Reissig: The Influence of Oscillations on Energy Estimates for Damped Wave Models with Time-dependent Propagation Speed and Dissipation.- A. H. Babayan and S. H. Abelyan: On a Dirichlet Problem for One Improperly Elliptic Equation.- N. Gialelis and I. G. Stratis: On the 1-dim DefocusingNLS Equation with Non-vanishing Initial Data at Infinity.- Y. E. Gliklikh: On Time-global Solutions of SDE Having Nowhere Vanishing Initial Densities.- F. A. Gómez and V. V. Kravchenko: On Transmutation Operators and Neumann Series of Bessel Functions Representations for Solutions of Linear Higher Order Differential Equations.- H.M. Hayrapetyan: On a Boundary Value Problem with Infinite Index.- O. Kudryavtsev and V. Rodochenko: A Numerical Realization of the Wiener-Hopf Method for the Kolmogorov Backward Equation.- A. Vatulyan and V. Yurov: On Waves Processes in Transversally-inhomogeneous Waveguides.- V. Yurko: Inverse Spectral Problems for Differential Systems.