@inbook{19b8f351a5874b928c2a6d490644ce8e,

title = "On Exceptional Extensions Close to the Generalized Friedrichs Extension of Symmetric Operators",

abstract = "If the Q-function Q corresponding to a closed symmetric operator S with defect numbers (1, 1) and one of its selfadjoint extensions belongs to the Kac class N1 then it is known that all except one of the Q-functions of S belong to N1, too. In this note the situation that the given Q-function does not belong to the class N1 is considered. If Q ∈ Np, i.e., if the restriction of the spectral measure of Q on the positive or the negative axis corresponds to an N1-function, then Q itself is the Q-function of the exceptional extension, and, hence, it is associated with the generalized Friedrichs extension of S. If Q or, equivalently, the spectral measure of Q is symmetric, or if the difference of Q and a symmetric Nevanlinna function belongs to the class N1 or Np, then Q is still exceptional in a wider sense. Similar results hold for the generalized Kreĭn-von Neumann extension of the symmetric operator.",

keywords = "Kac class, generalized Kreĭn-von Neumann extension, generalized Friedrichs extension, Q-function",

author = "Seppo Hassi and {de Snoo}, Henk and Henrik Winkler",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)",

year = "2007",

doi = "10.1007/978-3-7643-8270-4_7",

language = "English",

isbn = "978-3-7643-8269-8",

volume = "175",

series = "Operator Theory: Advances and Applications ",

publisher = "Birkhauser",

pages = "111--12--",

booktitle = "Operator Theory in Inner Product Spaces",

}