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Subject Item
dbr:Extensions_of_symmetric_operators
rdfs:label
Extensions of symmetric operators
rdfs:comment
In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self-adjoint extensions. This problem arises, for example, when one needs to specify domains of self-adjointness for formal expressions of observables in quantum mechanics. Other applications of solutions to this problem can be seen in various moment problems.
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dbc:Operator_theory dbc:Functional_analysis
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10858909
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1070868282
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dbr:Absolutely_continuous_function dbr:Self-adjoint dbc:Functional_analysis dbr:Contraction_(operator_theory) dbr:Momentum_operator dbr:Unbounded_operator dbr:Partial_isometry dbr:Accretive_operator dbr:Symmetric_operator dbr:Quantum_mechanics dbr:Observable dbr:Closable_operator dbr:Hellinger-Toeplitz_theorem dbr:Matrix_completion dbr:Functional_analysis dbr:Riesz_representation_theorem dbr:Hilbert_space dbr:Self-adjoint_operator dbr:Linear_operator dbr:Densely_defined dbr:Friedrichs_extension dbc:Operator_theory dbr:Bounded_operator dbr:Moment_problem dbr:Cayley_transform dbr:Closed_operator
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In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self-adjoint extensions. This problem arises, for example, when one needs to specify domains of self-adjointness for formal expressions of observables in quantum mechanics. Other applications of solutions to this problem can be seen in various moment problems. This article discusses a few related problems of this type. The unifying theme is that each problem has an operator-theoretic characterization which gives a corresponding parametrization of solutions. More specifically, finding self-adjoint extensions, with various requirements, of symmetric operators is equivalent to finding unitary extensions of suitable partial isometries.
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