Self-Adjoint Extensions with Friedrichs Lower Bound
نویسندگان
چکیده
منابع مشابه
Self-adjoint Extensions of Restrictions
We provide, by a resolvent Krĕın-like formula, all selfadjoint extensions of the symmetric operator S obtained by restricting the self-adjoint operator A : D(A) ⊆ H → H to the dense, closed with respect to the graph norm, subspace N ⊂ D(A). Neither the knowledge of S∗ nor of the deficiency spaces of S is required. Typically A is a differential operator and N is the kernel of some trace (restric...
متن کاملSelf-adjoint Extensions by Additive Perturbations
Let AN be the symmetric operator given by the restriction of A toN , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph norm on D(A), the operator domain of A. We show that any self-adjoint extension AΘ of AN such that D(AΘ)∩D(A) = N can be additively decomposed by the sum AΘ = Ā + TΘ, where both the operators Ā and TΘ...
متن کاملSelf - adjoint extensions and Signature Change
We study the selfadjoint extensions of the spatial part of the D'Alembert operator in a spacetime with two changes of signature. We identify a set of boundary conditions, parametrised by U (2) matrices, which correspond to Dirichlet boundary conditions for the fields, and from which we argue against the suggestion that regions of signature change can isolate singularities.
متن کاملUsing Self-adjoint Extensions in Shape Optimization
Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriat...
متن کاملResolvents of self-adjoint extensions with mixed boundary conditions
We prove a variant of Krein’s resolvent formula for self-adjoint extensions given by arbitrary boundary conditions. A parametrization of all such extensions is suggested with the help of two bounded operators instead of multivalued operators and selfadjoint linear relations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2020
ISSN: 1661-8254,1661-8262
DOI: 10.1007/s11785-020-01032-z