About: Extensions of symmetric operators

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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.

Attributes	Values
rdfs:label	Extensions of symmetric operators (en)
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. (en)
dcterms:subject	Operator theory Functional analysis
Wikipage page ID	10858909 (xsd:integer)
Wikipage revision ID	1070868282 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics Partial isometry Densely defined Riesz representation theorem Unbounded operator Operator theory Closable operator Closed operator Bounded operator Moment problem Contraction (operator theory) Linear operator Friedrichs extension Functional analysis Matrix completion Cayley transform Momentum operator Accretive operator Hilbert space Functional analysis Hellinger-Toeplitz theorem Self-adjoint operator Observable Symmetric operator Self-adjoint Absolutely continuous function
sameAs	Extensions of symmetric operators Extensions of symmetric operators Extensions of symmetric operators
dbp:wikiPageUsesTemplate	dbt:= dbt:Expand_section dbt:No_footnotes dbt:Short_description dbt:Abs dbt:Mset dbt:Functional_Analysis
has abstract	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. (en)
prov:wasDerivedFrom	wikipedia-en:Extensions_of_symmetric_operators?oldid=1070868282&ns=0
page length (characters) of wiki page	12978 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Extensions_of_symmetric_operators
is rdfs:seeAlso of	Unbounded operator Self-adjoint operator
is Link from a Wikipage to another Wikipage of	Mikhail Samuilovich Livsic Friedrichs extension Hamburger moment problem Stone's theorem on one-parameter unitary groups Cayley transform
is foaf:primaryTopic of	wikipedia-en:Extensions_of_symmetric_operators

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