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000726975 019__ $$a910706958
000726975 020__ $$a9783319164892$$qelectronic book
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000726975 020__ $$z9783319164885
000726975 0247_ $$a10.1007/978-3-319-16489-2$$2doi
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000726975 049__ $$aISEA
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000726975 1001_ $$aSakhnovich, L. A.,$$eauthor.
000726975 24510 $$aIntegral equations with difference kernels on finite intervals$$h[electronic resource] /$$cLev A. Sakhnovich.
000726975 250__ $$aSecond edition, revised and extended
000726975 264_1 $$aCham :$$bBirkhäuser,$$c[2015]
000726975 300__ $$a1 online resource.
000726975 336__ $$atext$$btxt$$2rdacontent
000726975 337__ $$acomputer$$bc$$2rdamedia
000726975 338__ $$aonline resource$$bcr$$2rdacarrier
000726975 4901_ $$aOperator theory: advances and applications,$$x2296-4878 ;$$vvolume 84
000726975 504__ $$aIncludes bibliographical references and index.
000726975 5050_ $$aPreface to the second edition -- Introduction to the first edition -- 1.Invertible Operator with a Difference Kernel -- 2.Equations of the First Kind with a Difference Kernel -- 3.Examples and Applications -- 4.Eigensubspaces and Fourier Transform -- 5.Integral Operators with W-Difference Kernels -- 6.Problems of Communication Theory -- 7.Levy Processes: Convolution-Type Form of the Infinitesimal Generator -- 8.On the Probability that the Levy Process (Class II) Remains within the Given Domain -- 9.Triangular Factorization and Cauchy Type Levy Processes -- 10.Levy Processes with Summable Levy Measures, Long Time Behavior -- 11.Open Problems -- Commentaries and Remarks -- Bibliography -- Glossary -- Index.
000726975 506__ $$aAccess limited to authorized users.
000726975 520__ $$aThis book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener?E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.
000726975 588__ $$aOnline resource; title from PDF title page (viewed May 14, 2015).
000726975 650_0 $$aIntegral equations.
000726975 650_0 $$aFinite differences.
000726975 77608 $$iPrint version:$$z9783319164885
000726975 830_0 $$aOperator theory. advances and applications ;$$vv. 84.
000726975 852__ $$bebk
000726975 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-16489-2$$zOnline Access$$91397441.1
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