Transmutation Operators and Applications

Abstract

Part I: Transmutations, Integral Equations and Special Functions.- Some Recent Developments in the Transmutation Operator Approach.- Transmutation Operators and Their Applications.- Hankel Generalized Convolutions with the Associated Legendre Functions in the Kernel and Their Applications.- Second Type Neumann Series Related to Nicholson's and to Dixon-Ferrar Formula.- On Some Generalizations of the Properties of the Multidimensional Generalized Erdelyi-Kober Operators and Their Applications.- Alternative Approach to Miller-Paris Transformations and Their Extensions.- Transmutation Operators For Ordinary Dunkl-Darboux Operators.- Theorems on Restriction of Fourier-Bessel and Multidimensional Bessel Transforms to Spherical Surfaces.- Necessary Condition for the Existence of an Intertwining Operator and Classification of Transmutations on Its Basis.- Polynomial Quantization on Line Bundles.- Fourier-Bessel Transforms of Measures and Qualitative Properties of Solutions of Singular Differential Equations.- Inversion of Hyperbolic B-Potentials.- One-Dimensional and Multi-Dimensional Integral Transforms of Buschman-Erdelyi Type with Legendre Functions in Kernels.- Distributions, Non-smooth Manifolds, Transmutations and Boundary Value Problems.- Part II: Transmutations in ODEs, Direct and Inverse Problems.- On a Transformation Operator Approach in the Inverse Spectral Theory of Integral and Integro-Differential Operators.- Expansion in Terms of Appropriate Functions and Transmutations.- Transmutation Operators as a Solvability Concept of Abstract Singular Equations.- On the Bessel-Wright Operator and Transmutation with Applications.- On a Method of Solving Integral Equation of Carleman Type on the Pair of Segments.- Transmutation Operators Boundary Value Problems.- Solution of Inverse Problems for Differential Operators with Delay.- Part III: Transmutations for Partial and Fractional Differential Equations.- Transmutations of the Composed Erdelyi-Kober Fractional Operators and Their Applications.- Distributed Order Equations in Banach Spaces with Sectorial Operators.- Transformation Operators for Fractional Order Ordinary Differential Equations and Their applications.- Strong Solutions of Semilinear Equations with Lower Fractional Derivatives.- Mean Value Theorems and Properties of Solutions of Linear Differential Equations.- Transmutations for Multi-Term Fractional Operators.- Fractional Bessel Integrals and Derivatives on Semi-axes.- The Fractional Derivative Expansion Method in Nonlinear Dynamics of Structures: A Memorial Essay.- Boundary Value Problem with Integral Condition for the Mixed Type Equation with a Singular Coefficient.