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On problems for linear differential operations. (English. Russian original) Zbl 0618.35018

Math. USSR, Sb. 57, 411-419 (1987); translation from Mat. Sb., Nov. Ser. 129(171), No. 3, 397-406 (1986).
For a differential operator \({\mathcal L}\) in a domain V the minimal and maximal extensions are defined respectively as \(L_ 0\) the closure of \({\mathcal L}: C_ 0^{\infty}(V)\to L^ 2(V)\) and \(\tilde L=({\mathcal L}^ t_ 0)\) where \({\mathcal L}^ t\) is the transpose (formal adjoint) of \({\mathcal L}\). The paper deals with numerous general properties of operators S: D(S)\(\subset L^ 2(V)\to L^ 2(V)\) satisfying one or both of the inclusions \(S\subset \tilde L\) or \(L_ 0\subset S\); such operators correspond to various side conditions, not necessarily boundary conditions, associated with the operator.
Reviewer: P.Szeptycki

MSC:

35G15 Boundary value problems for linear higher-order PDEs
47A20 Dilations, extensions, compressions of linear operators
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