NUMERICAL METHOD FOR REDUCING A DIFFERENTIAL OPERATOR
Keywords:
linear operator, maximal operator, correct restriction, correct extension, Hilbert space, continuous transformation, adjoint operatorAbstract
This article explores abstract operator-theoretic approaches to describing well-posed restrictions and extensions of linear differential operators in Hilbert spaces. The authors prove two fundamental theorems establishing a one-to-one correspondence between well-posed restrictions of a maximal operator and classes of continuous transformations acting on the kernel of the operator or its domain. A constructive connection between the resulting formulas and the theory of adjoint operators is demonstrated, allowing for the effective characterization of well-posed boundary value problems (including Bitsadze-Samarskii-type problems) for minimal differential operators.
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