Modern Methods In Operator Theory And Harmonic Analysis: Otha 2018, Rostov-on-don, Russia, April 22-27, Selected, Revised And Extended Contributions (springer Proceedings In Mathematics & Statistics)

"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"--Page 4 of cover Front Matter ....Pages i-xv Front Matter ....Pages 1-1 Some General Properties of Operators in Morrey-Type Spaces (Mikhail L. Goldman, Elza Bakhtigareeva)....Pages 3-34 Characterization of Parabolic Fractional Maximal Function and Its Commutators in Orlicz Spaces (Vagif S. Guliyev, Ahmet Eroglu, Gulnara A. Abasova)....Pages 35-49 Finite Trees Inside Thin Subsets of \({\mathbb R}^{d}\) (A. Iosevich, K. Taylor)....Pages 51-56 Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Functions of Hölder Type (Alexey Karapetyants, Joel E. Restrepo)....Pages 57-66 Generalized Fourier Series by the Double Trigonometric System (K. S. Kazarian)....Pages 67-79 Hardy Type Inequalities in the Category of Hausdorff Operators (Elijah Liflyand)....Pages 81-91 Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One (Helmuth R. Malonek, Isabel Cação, M. Irene Falcão, Graça Tomaz)....Pages 93-115 Paraproduct in Besov–Morrey Spaces (Yoshihiro Sawano)....Pages 117-133 Front Matter ....Pages 135-135 Analogs of the Khintchin—Kolmogorov Inequalities in Discrete Morrey Spaces (Evgenii I. Berezhnoĭ)....Pages 137-151 Mellin Convolution Equations (Roland Duduchava)....Pages 153-174 Integral Operators of the \(\mathcal {L}\)-Convolution Type in the Case of a Reflectionless Potential (Davresh Hasanyan, Armen Kamalyan, Martin Karakhanyan, Ilya M. Spitkovsky)....Pages 175-197 Spectral Theory for Nonlinear Operators: Quadratic Case (Yakov Krasnov)....Pages 199-216 Factorization of Order Bounded Disjointness Preserving Multilinear Operators (Anatoly G. Kusraev, Zalina A. Kusraeva)....Pages 217-236 Robbins–Monro Conditions for Persistent Exploration Learning Strategies (Dmitry B. Rokhlin)....Pages 237-247 On Widths of Invariant Sets (Ekaterina Shulman)....Pages 249-261 The Distance Function and Boundedness of Diameters of the Nearest Elements (Igor’ G. Tsar’kov)....Pages 263-272 Front Matter ....Pages 273-273 The Influence of Oscillations on Energy Estimates for Damped Wave Models with Time-dependent Propagation Speed and Dissipation (Halit Sevki Aslan, Michael Reissig)....Pages 275-316 On a Dirichlet Problem for One Improperly Elliptic Equation (Armenak H. Babayan, Seyran H. Abelyan)....Pages 317-335 On the 1-dim Defocusing NLS Equation with Non-vanishing Initial Data at Infinity (Nikolaos Gialelis, Ioannis G. Stratis)....Pages 337-362 On Time-Global Solutions of SDE Having Nowhere Vanishing Initial Densities (Yuri E. Gliklikh)....Pages 363-370 On Transmutation Operators and Neumann Series of Bessel Functions Representations for Solutions of Linear Higher Order Differential Equations (Flor A. Gómez, Vladislav V. Kravchenko)....Pages 371-385 On a Boundary Value Problem with Infinite Index (H. M. Hayrapetyan)....Pages 387-397 A Numerical Realization of the Wiener–Hopf Method for the Kolmogorov Backward Equation (Oleg Kudryavtsev, Vasily Rodochenko)....Pages 399-426 On Waves Processes in Transversally-Inhomogeneous Waveguides (Alexander Vatulyan, Victor Yurov)....Pages 427-449 Inverse Spectral Problems for Differential Systems (Vjacheslav Anatoljevich Yurko)....Pages 451-475 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 Besov-Morrey Spaces -- Part II: Functional Analysis and Operator Theory -- E.I. Berezhnoĭ: 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 Defocusing NLS 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