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008 170212s2015 gw | s |||| 0|eng d
020 _a9783319164892
_9978-3-319-16489-2
024 7 _a10.1007/978-3-319-16489-2
_2doi
035 _ato000559299
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA431
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.45
_223
100 1 _aSakhnovich, Lev A.
_eauthor.
_9465637
245 1 0 _aIntegral Equations with Difference Kernels on Finite Intervals
_helectronic resource
_bSecond Edition, Revised and Extended /
_cby Lev A. Sakhnovich.
250 _a2nd revised and extended ed. 2015.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2015.
300 _aXVIII, 226 p. 2 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aOperator Theory: Advances and Applications,
_x0255-0156 ;
_v84
505 0 _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.
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.
650 0 _amathematics.
_9566183
650 0 _aIntegral equations.
_9566371
650 0 _aOperator theory.
_9566350
650 0 _aProbabilities.
_9295556
650 1 4 _aMathematics.
_9566184
650 2 4 _aIntegral Equations.
_9566372
650 2 4 _aOperator Theory.
_9566351
650 2 4 _aProbability Theory and Stochastic Processes.
_9303734
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aOperator Theory: Advances and Applications,
_9566535
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-16489-2
912 _aZDB-2-SMA
999 _c414029