By Z. S. Marchenko, V. A. Agranovich
Half 1. The boundary-value challenge with no singularities --
I. specific recommendations of the procedure with no singularities --
II. The spectrum and scattering matrix for the boundary-value challenge with no singularities --
III. the elemental equation --
IV. Parseval's equality --
V. The inverse challenge --
Part 2. The boundary-value challenge with singularities --
VI. specific transformation operators --
VII. Spectral research of the boundary-value challenge with singularities --
VIII. Reconstruction of the singular boundary-value challenge from its scattering info --
Appendix I. at the attribute homes of the scattering info of the boundary-value challenge with no singularities --
Appendix II. Refinement of definite inequalities.
Read Online or Download The inverse problem of scattering theory PDF
Similar mathematics_1 books
Dieses erfolgreiche einf? hrende Lehrbuch liegt nun in der 10. Auflage vor. Es zeichnet sich durch eine exakte und anschauliche Darstellung aus. Der Lehrstoff ist klar gegliedert und intestine strukturiert. Er wird durch eine F? lle von Beispielen und Abbildungen veranschaulicht und vertieft. Zahlreiche Aufgaben mit L?
Probabilistic Expert Systems (CBMS-NSF Regional Conference Series in Applied Mathematics)
Probabilistic professional structures emphasizes the fundamental computational ideas that make probabilistic reasoning possible in specialist platforms. the foremost to computation in those platforms is the modularity of the probabilistic version. Shafer describes and compares the vital architectures for exploiting this modularity within the computation of past and posterior percentages.
Surveys in Differential-Algebraic Equations III
The current quantity contains survey articles on a number of fields of Differential-Algebraic Equations (DAEs), that have common purposes in managed dynamical structures, particularly in mechanical and electric engineering and a powerful relation to (ordinary) differential equations. the person chapters offer studies, shows of the present country of analysis and new innovations in - Flexibility of DAE formulations - Reachability research and deterministic international optimization - Numerical linear algebra tools - Boundary price difficulties the implications are provided in an obtainable kind, making this publication compatible not just for energetic researchers but in addition for graduate scholars (with a very good wisdom of the fundamental ideas of DAEs) for self-study.
- Contributions to Statistics
- Simulation-Driven Modeling and Optimization: ASDOM, Reykjavik, August 2014
- Noneuclidean Geometry
- Les mathématiques pour tous
Additional resources for The inverse problem of scattering theory
Example text
J K(t, s)e-iA(s-t) ds dt. = -µ < 0. _ ev,(x)a2(x). 1) and the fact that f'a(x) dx s a1(a) < oo, a j :z;l+aa2(x) J a(x) dx J tl+a IV(t) I dt dx s Also, for b (a>O). t IV(t) I dt + -1 ·. b ei+a jV(t) I dt+ 2µ 2µ ::s - f jV(t) I dt+-1 fb xiH jV(x) I dx. t jV(t) I dt < 00° (a> 0). ) I dx< oo (a>O). ) (Im A. = 0, A. ¥=: 0). 2) and has the required asymptotic behavior at infinity. ) for sufficiently large J. A. A. ) dt. A. ) = I - 2 f f . A. ) dt. h It is easy to show by· the method of successive approximations that a solution to this equation exists in the interval h s x < oo.
I "" s; t): ! V(s) Ids = x+t -2- x+t , K1(x. t) ! =:;; ! -J-iv<·l Id. ·+r ! V(s) Ids x+t 21 2l a (s+u) 2 du s. V(s)lds = 21 a (x+t). · 2 a1 (x). __ 2 a (x+t) a1'm(x)! 2 (m = 0, 1, 2, .... · I. 3) holds for its sum K(x, t). 6). Finally, " t JO'(u} du = xJ du uJ jV(t) I dt = xJ jV(t) I dt Jx du = x = f (t-x) IV(t} I dt s 0'1 (x). 3), we find that f 00 I K(x, t) I dt ,,;;; 21 eO",(x) x f O' (x+t) . 5)). 1 ds J I K(s, u) I du seO",(x)O'~(x) Dt. h It is easy to show by· the method of successive approximations that a solution to this equation exists in the interval h s x < oo. provided h is positive and is such that 21~1 f jV(t) I dt=q< I. )ldt+ x X. t IV(t) I. 4}. l) = eiAx [l + o(x-1-11)] (x -oo). l) = i,leiAx[l +o(x-1-11)] (x - oo). A. l) dt. t] dt s I. 2~ f [ + 2~ b (1 h a)x6e-2f&X b ::S x . 1 V(x) :S J IV(t) I dt + xlH IV(x) I dx, . t h x b dx x h ~ J I h (1 + a)x"e-2f&X and for b . 1), x J xi+"e-21'X dx J e2P-t IV(t) ldt h < oo.