大葉大學圖書館 |

Integral equations with difference kernels on finite intervals[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.45
書名/作者:	Integral equations with difference kernels on finite intervals/ by Lev A. Sakhnovich.
作者:	Sakhnovich, Lev A.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xviii, 226 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Finite differences.
標題:	Mathematics.
標題:	Integral Equations.
標題:	Operator Theory.
標題:	Probability Theory and Stochastic Processes.
標題:	Integral equations.
ISBN:	9783319164892 (electronic bk.)
ISBN:	9783319164885 (paper)
內容註:	Preface 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.
摘要、提要註:	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 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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-16489-2

Integral equations with difference kernels on finite intervals[electronic resource] /
Sakhnovich, Lev A.

Integral equations with difference kernels on finite intervals[electronic resource] /by Lev A. Sakhnovich. - 2nd ed, revised and extended. - Cham :Springer International Publishing :2015. - xviii, 226 p. :ill., digital ;24 cm. - Operator theory: advances and applications,v.840255-0156 ;. - Operator theory: advances and applications ;v.219..

Preface 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.

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 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.

ISBN: 9783319164892 (electronic bk.)

Standard No.: 10.1007/978-3-319-16489-2doiSubjects--Topical Terms:

404854
Finite differences.

LC Class. No.: QA431

Dewey Class. No.: 515.45

Integral equations with difference kernels on finite intervals[electronic resource] /
LDR:03165nmm a2200337 a 4500 001 438995
003 DE-He213
005 20160105141839.0
006 m d
007 cr nn 008maaau
008 160315s2015 gw s 0 eng d
020 $a 9783319164892 (electronic bk.)
020 $a 9783319164885 (paper)
024 7 $a 10.1007/978-3-319-16489-2 $2 doi
035 $a 978-3-319-16489-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA431
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.45 $2 23
090 $a QA431 $b .S158 2015
100 1 $a Sakhnovich, Lev A. $3 626561
245 1 0 $a Integral equations with difference kernels on finite intervals $h [electronic resource] / $c by Lev A. Sakhnovich.
250 $a 2nd ed, revised and extended.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a xviii, 226 p. : $b ill., digital ; $c 24 cm.
490 1 $a Operator theory: advances and applications, $x 0255-0156 ; $v v.84
505 0 $a Preface 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 $a 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 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 $a Finite differences. $3 404854
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Integral Equations. $3 468445
650 2 4 $a Operator Theory. $3 464906
650 2 4 $a Probability Theory and Stochastic Processes. $3 463894
650 0 $a Integral equations. $3 183249
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Operator theory: advances and applications ; $v v.219. $3 465786
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16489-2
950 $a Mathematics and Statistics (Springer-11649)