Transmutation Operators and Applications / edited by Vladislav V. Kravchenko, Sergei M. Sitnik.

1st ed. 2020.
Cham : Springer International Publishing : Imprint: Birkhäuser, 2020.
Mathematics and Statistics (Springer-11649)
Trends in mathematics 2297-0215
Trends in Mathematics, 2297-0215
1 online resource (XVII, 686 pages) : 5 illustrations, 1 illustrations in color.
Differential equations.
Differential equations, Partial.
Integral transforms.
Calculus, Operational.
Functions of real variables.
Potential theory (Mathematics).
Local subjects:
Ordinary Differential Equations. (search)
Partial Differential Equations. (search)
Integral Transforms, Operational Calculus. (search)
Real Functions. (search)
Potential Theory. (search)
System Details:
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Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject. .
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 Erdélyi-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-Erdélyi 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 Erdélyi-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. .
Kravchenko, Vladislav V. editor., Editor,
Sitnik, Sergei M. editor., Editor,
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