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|a Transmutation operators and applications
|h [electronic resource] /
|c Vladislav V. Kravchenko, Sergei M. Sitnik, editors.
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| 260 |
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|a Cham :
|b Birkhäuser,
|c 2020.
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| 300 |
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|a 1 online resource ( 685 p..)
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| 490 |
1 |
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|a Trends in Mathematics
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| 500 |
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|a Description based upon print version of record.
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0 |
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|a Intro -- Preface -- Contents -- Part I Transmutations, Integral Equations and Special Functions -- Some Recent Developments in the Transmutation Operator Approach -- References -- Transmutation Operators and Their Applications -- 1 Introduction -- 2 Existence and Construction of Transmutations -- 2.1 Classical Transmutations -- 2.2 Transmutations by Paley-Wiener Theorem -- 2.3 Rigged Hilbert Spaces -- 2.4 Transmutation with Distinct Spectra -- 2.5 Transmutation with Disjoint Spectra -- 3 Transmutation for Strings -- 3.1 Transmutation for Strings -- 3.2 Adding a Potential -- 3.3 Examples
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|a 4 Applications -- 4.1 The Gelfand-Levitan Theory -- 4.2 Gelfand-Levitan Revisited -- 4.3 Transmutation Between Orthogonal Polynomials -- 4.3.1 Example -- 4.4 Direct Reconstruction of the Spectral Function -- 4.5 The Lieb and Thirring Constant -- 4.6 Gelfand-Levitan for the String -- 4.6.1 The Transformation Operator -- 4.7 Sampling and Transmutation -- 4.8 Computational Spectral Theory -- References -- Hankel Generalized Convolutions with the Associated Legendre Functions in the Kernel and Their Applications -- 1 Introduction -- 2 Properties and Estimates for the Convolution's Kernel
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|a 3 Mapping Properties of the Generalized Convolutions -- 4 Integral Transforms Related to the Hankel Polyconvolution -- 5 Examples -- References -- Second Type Neumann Series Related to Nicholson's and to Dixon-Ferrar Formula -- 1 Introduction to Nicholson's Formula -- 2 Preparation: Euler-Maclaurin Summation Formula, Dirichlet Series and Cahen's Formula -- 3 Main Results: Accessum per Definitionem -- 4 Main Results: The Dixon-Ferrar Formula -- 5 Discussion: Open Problems -- References
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|a On Some Generalizations of the Properties of the Multidimensional Generalized Erdélyi-Kober Operators and Their Applications -- 1 Introduction -- 2 Generalization of the Properties of the Generalized Erdelyi-Kober Operator -- 3 Applications -- Appendix: Integral Transform Composition Method (ITCM) in Transmutation Theory: How It Works -- What is ITCM and How It Works? -- Application of ITCM to Index Shift B-Hyperbolic Transmutations -- Application of Transmutations Obtained by ITCM to Integral Representations of Solutions to Hyperbolic Equations with Bessel Operators -- References
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|a Alternative Approach to Miller-Paris Transformations and Their Extensions -- 1 Introduction and Preliminaries -- 2 Miller-Paris Transformations: General Case -- 3 Miller-Paris Transformations: Degenerate Case -- References -- Transmutation Operators For Ordinary Dunkl-Darboux Operators -- 1 Introduction -- 2 Dunkl-Darboux Operators -- 3 Darboux Transmutations for High Order Differential Operators -- 4 Integral Dunkl-Darboux Transmutations -- 5 Transmutation Operators for Dunkl-Darboux Operators in Cherednik Algebra -- 6 Recurrence Equations
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| 500 |
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|a 7 Transmutation Operators for Dunkl-Darboux Operators in Cherednik Pseudoalgebra
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| 533 |
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|a Electronic reproduction.
|b Ann Arbor, MI
|n Available via World Wide Web.
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| 650 |
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0 |
|a Transmutation operators.
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| 700 |
1 |
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|a Kravchenko, Vladislav V.
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| 700 |
1 |
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|a Sitnik, Sergei M.
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| 710 |
2 |
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|a ProQuest (Firm)
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| 776 |
0 |
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|i Print version:
|a Kravchenko, Vladislav V.
|t Transmutation Operators and Applications
|d Cham : Springer Basel AG,c2020
|z 9783030359133
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| 830 |
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0 |
|a Trends in mathematics.
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| 856 |
4 |
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|u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=6174004
|z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)
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