{"product_id":"partial-differential-equations-viii-overdetermined-systems-dissipative-singular-schrodinger-operator-index-theory-von-m-a-shubin-hrsg","title":"Partial Differential Equations VIII","description":"\u003cp\u003eConsider a linear partial differential operator A that maps a vector-valued function Y = (Yl,\"\" Ym) into a vector-valued function I = (h,···, II). We assume at first that all the functions, as well as the coefficients of the differen­ tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR , and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A\" such that AA\" = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func­ tion Y into the vector-valued function (8y\/8x!, 8y\/8x2, 8y\/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642489464\"\u003e\u003ch3\u003eOverdetermined Systems Dissipative Singular Schrödinger Operator Index Theory\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642489464","offer_id":39438273773661,"sku":"9783642489464","price":96.29,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/33981a6c-b511-4521-b4ac-5c8196af02e7.jpg?v=1772172250","url":"https:\/\/shop.autorenwelt.de\/en\/products\/partial-differential-equations-viii-overdetermined-systems-dissipative-singular-schrodinger-operator-index-theory-von-m-a-shubin-hrsg","provider":"Autorenwelt Shop","version":"1.0","type":"link"}