{"product_id":"9780080537733","title":"Non-Self-Adjoint Boundary Eigenvalue Problems","description":"This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and \u003ci\u003en\u003c\/i\u003e-th order ordinary differential equations.\u003cbr\u003eIn 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every \u003ci\u003en\u003c\/i\u003e-th order differential equation is equivalent\u003cbr\u003eto a first order system, the main techniques are developed for systems. Asymptotic fundamental\u003cbr\u003esystems are derived for a large class of systems of differential equations. Together with boundary\u003cbr\u003econditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.\u003cbr\u003eThe contour integral method and estimates of the resolvent are used to prove expansion theorems.\u003cbr\u003eFor Stone regular problems, not all functions are expandable, and again relatively easy verifiable\u003cbr\u003econditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.\u003cbr\u003eChapter 10 deals exclusively  with applications; in nine sections, various concrete problems such as\u003cbr\u003ethe Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.\u003cp\u003e\u003cbr\u003e\u003cbr\u003eKey features:\u003cbr\u003e\u003cbr\u003e• Expansion Theorems for Ordinary Differential Equations \u003cbr\u003e• Discusses Applications to Problems from Physics and Engineering \u003cbr\u003e• Thorough Investigation of Asymptotic Fundamental Matrices and Systems \u003cbr\u003e• Provides a Comprehensive Treatment \u003cbr\u003e• Uses the Contour Integral Method \u003cbr\u003e• Represents the Problems as Bounded Operators \u003cbr\u003e• Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":47079402635504,"sku":"9780080537733","price":235.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780080537733_p0.jpg?v=1763637544","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780080537733","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}