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dc.contributor.authorCojuhari, P.en_US
dc.contributor.authorGheondea, A.en_US
dc.date.accessioned2016-02-08T11:02:20Z
dc.date.available2016-02-08T11:02:20Z
dc.date.issued2014en_US
dc.identifier.issn0378-620X
dc.identifier.urihttp://hdl.handle.net/11693/26610
dc.description.abstractWe obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. We provide a model and an abstract theorem as well for a triplet of closely embedded Hilbert spaces associated to positive selfadjoint operator H, that is called the Hamiltonian of the system, which is supposed to be one-to-one but may not have a bounded inverse. Existence and uniqueness results, as well as left-right symmetry, for these triplets of closely embedded Hilbert spaces are obtained. We motivate this abstract theory by a diversity of problems coming from homogeneous or weighted Sobolev spaces, Hilbert spaces of holomorphic functions, and weighted L2 spaces. An application to weak solutions for a Dirichlet problem associated to a class of degenerate elliptic partial differential equations is presented. In this way, we propose a general method of proving the existence of weak solutions that avoids coercivity conditions and Poincaré–Sobolev type inequalities. © 2014, Springer Basel.en_US
dc.language.isoEnglishen_US
dc.source.titleIntegral Equations and Operator Theoryen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00020-014-2195-0en_US
dc.subjectClosed embeddingen_US
dc.subjectDegenerate elliptic operatorsen_US
dc.subjectDirichlet problemen_US
dc.subjectHamiltonianen_US
dc.subjectkernel operatoren_US
dc.subjectRigged Hilbert spacesen_US
dc.subjectTriplet of Hilbert spacesen_US
dc.subjectWeak solutionsen_US
dc.titleTriplets of closely embedded Hilbert spacesen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage1en_US
dc.citation.epage33en_US
dc.citation.volumeNumber81en_US
dc.citation.issueNumber1en_US
dc.identifier.doi10.1007/s00020-014-2195-0en_US
dc.publisherSpringeren_US
dc.identifier.eissn1420-8989


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