Transmutation Operators and Applications
Transmutation Operators and Applications

Author: Vladislav V. Kravchenko

Publisher: Springer Nature

Published: 2020-04-11

Total Pages: 685

ISBN-13: 303035914X

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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.

Transmutation Operators and Applications
Transmutation Operators and Applications

Author: Vladislav V. Kravchenko

Publisher: Birkhäuser

Published: 2020-05-19

Total Pages: 686

ISBN-13: 9783030359133

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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.

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics
Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Author: Elina Shishkina

Publisher: Academic Press

Published: 2020-07-24

Total Pages: 594

ISBN-13: 0128204079

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Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. - Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods - Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details - Enables researchers, lecturers and students to find material under the single "roof"

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics
Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Author: Elina Shishkina

Publisher: Academic Press

Published: 2020-07-24

Total Pages: 592

ISBN-13: 0128197811

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Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights.

Direct and Inverse Sturm-Liouville Problems
Direct and Inverse Sturm-Liouville Problems

Author: Vladislav V. Kravchenko

Publisher: Springer Nature

Published: 2020-07-28

Total Pages: 155

ISBN-13: 3030478491

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This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Direct and Inverse Sturm-Liouville Problems
Direct and Inverse Sturm-Liouville Problems

Author: Vladislav V. Kravchenko

Publisher: Birkhäuser

Published: 2020-08-18

Total Pages: 154

ISBN-13: 9783030478483

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This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Applications of Hypergroups and Related Measure Algebras
Applications of Hypergroups and Related Measure Algebras

Author:

Publisher: American Mathematical Soc.

Published: 1995-02-28

Total Pages: 458

ISBN-13: 0821802976

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`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.