Integral Equations with Difference Kernels on Finite Intervals Second Edition, Revised and Extended
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Sprache:Englisch
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Verlag:Springer
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Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
18.05.2015
Abbildungen
XVIII, 2 illus., schwarz-weiss Illustrationen
Verlag
SpringerSeitenzahl
226
Maße (L/B/H)
24.1/16/1.9 cm
Gewicht
479 g
Auflage
2nd revised and extended ed. 2015
Sprache
Englisch
ISBN
978-3-319-16488-5
This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression thathas proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.
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