Rudolf Gorenflo's Books

Mittag-Leffler Functions, Related Topics and Applications

By: Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei V. Rogosin

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Mittag-Leffler Functions, Related Topics and Applications

By: Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei V. Rogosin

As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

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Page Count

454

Publisher

Springer

Published Date

ISBN 10

3662439301

ISBN 13

9783662439302

Abel Integral Equations

Analysis and Applications

By: Rudolf Gorenflo,Sergio Vessella

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Abel Integral Equations

Analysis and Applications

By: Rudolf Gorenflo,Sergio Vessella

In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.

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Page Count

225

Publisher

Springer

Published Date

ISBN 10

3540469494

ISBN 13

9783540469490

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

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Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.

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Page Count

188

Publisher

Springer

Published Date

ISBN 10

3540456589

ISBN 13

9783540456582

Abel Integral Equations

Analysis and Applications

By: Rudolf Gorenflo,Sergio Vessella

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Abel Integral Equations

Analysis and Applications

By: Rudolf Gorenflo,Sergio Vessella

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Solve jigsaw puzzle

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Page Count

225

Publisher

Springer

Published Date

ISBN 10

3540469494

ISBN 13

9783540469490

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

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Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

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N/A

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Solve jigsaw puzzle

Age

Page Count

188

Publisher

Springer

Published Date

ISBN 10

3540456589

ISBN 13

9783540456582

Book's by Rudolf Gorenflo

Mittag-Leffler Functions, Related Topics and Applications

Mittag-Leffler Functions, Related Topics and Applications

Abel Integral Equations

Abel Integral Equations

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

Abel Integral Equations

Abel Integral Equations

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

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