Transmutation Operators and Applications. 1st ed. 2020

種類:

電子ブック

責任表示:

edited by Vladislav V. Kravchenko, Sergei M. Sitnik

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• Kravchenko, Vladislav V.
• Sitnik, Sergei M.
• SpringerLink (Online service)

シリーズ名:

Trends in Mathematics ;

ISBN:

9783030359140 [303035914X]    

注記:

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 Equatio
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. .

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