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Transmutation Operators and Applications

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  • © 2020

Overview

Editors:
  1. Vladislav V. Kravchenko

    1. Department of Mathematics, Center for Research and Advanced Studies, National Polytechnic Institute, Queretaro, Mexico

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  2. Sergei M. Sitnik

    1. Belgorod State National Research University (BelGU), Belgorod, Russia

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    You can also search for this editor in PubMed   Google Scholar

  • Compiles a wide range of applications of transmutation theory in one volume
  • Leads to new research areas and problems
  • Provides material that may be used for teaching, as parts of university courses and programs

Part of the book series: Trends in Mathematics (TM)

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Transmutations, Integral Equations and Special Functions

    1. Front Matter

      Pages 1-1
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    2. Some Recent Developments in the Transmutation Operator Approach

      • Vladislav V. Kravchenko, Sergei M. Sitnik
      Pages 3-9

    3. Transmutation Operators and Their Applications

      • Amin Boumenir, Vu Kim Tuan
      Pages 11-47

    4. Hankel Generalized Convolutions with the Associated Legendre Functions in the Kernel and Their Applications

      • Lyubov Britvina
      Pages 49-66

    5. Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula

      • Djurdje Cvijović, Tibor K. Pogány
      Pages 67-84

    6. On Some Generalizations of the Properties of the Multidimensional Generalized Erdélyi–Kober Operators and Their Applications

      • Sh. T. Karimov, S. M. Sitnik
      Pages 85-115

    7. Alternative Approach to Miller-Paris Transformations and Their Extensions

      • D. B. Karp, E. G. Prilepkina
      Pages 117-140

    8. Transmutation Operators For Ordinary Dunkl–Darboux Operators

      • S. P. Khekalo, V. V. Meshcheryakov, K. O. Politov
      Pages 141-158

    9. Theorems on Restriction of Fourier–Bessel and Multidimensional Bessel Transforms to Spherical Surfaces

      • A. A. Larin
      Pages 159-170

    10. Necessary Condition for the Existence of an Intertwining Operator and Classification of Transmutations on Its Basis

      • Sergei M. Sitnik, Viktor I. Makovetsky
      Pages 171-191

    11. Polynomial Quantization on Line Bundles

      • V. F. Molchanov
      Pages 193-205

    12. Fourier–Bessel Transforms of Measures and Qualitative Properties of Solutions of Singular Differential Equations

      • A. B. Muravnik
      Pages 207-235

    13. Inversion of Hyperbolic B-Potentials

      • E. L. Shishkina
      Pages 237-291

    14. One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels

      • Sergei M. Sitnik, Oksana V. Skoromnik
      Pages 293-319

    15. Distributions, Non-smooth Manifolds, Transmutations and Boundary Value Problems

      • Vladimir B. Vasilyev
      Pages 321-334
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Keywords

About this book

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. 


Editors and Affiliations

  • Department of Mathematics, Center for Research and Advanced Studies, National Polytechnic Institute, Queretaro, Mexico

    Vladislav V. Kravchenko

  • Belgorod State National Research University (BelGU), Belgorod, Russia

    Sergei M. Sitnik

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