• About
  • Policies
  • What is openaccess
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Mathematics
      • View Item
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Mathematics
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Triplets of closely embedded Hilbert spaces

      Thumbnail
      View / Download
      498.5 Kb
      Author
      Cojuhari, P.
      Gheondea, A.
      Date
      2014
      Source Title
      Integral Equations and Operator Theory
      Print ISSN
      0378-620X
      Electronic ISSN
      1420-8989
      Publisher
      Springer
      Volume
      81
      Issue
      1
      Pages
      1 - 33
      Language
      English
      Type
      Article
      Item Usage Stats
      115
      views
      87
      downloads
      Abstract
      We 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.
      Keywords
      Closed embedding
      Degenerate elliptic operators
      Dirichlet problem
      Hamiltonian
      kernel operator
      Rigged Hilbert spaces
      Triplet of Hilbert spaces
      Weak solutions
      Permalink
      http://hdl.handle.net/11693/26610
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s00020-014-2195-0
      Collections
      • Department of Mathematics 614
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartments

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 1771
      Copyright © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy