000 02325nam a22003855i 4500
001 978-3-8348-8327-8
003 DE-He213
005 20140220083819.0
007 cr nn 008mamaa
008 110728s2011 gw | s |||| 0|eng d
020 _a9783834883278
_9978-3-8348-8327-8
024 7 _a10.1007/978-3-8348-8327-8
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
082 0 4 _a510
_223
100 1 _aNesemann, Jan.
_eauthor.
245 1 0 _aPT-Symmetric Schrödinger Operators with Unbounded Potentials
_h[electronic resource] /
_cby Jan Nesemann.
264 1 _aWiesbaden :
_bVieweg+Teubner,
_c2011.
300 _aVIII, 83p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
520 _aFollowing the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all – provided one is familiar with the theory of self-adjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum.
650 0 _aMathematics.
650 1 4 _aMathematics.
650 2 4 _aMathematics, general.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783834817624
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-8348-8327-8
912 _aZDB-2-SMA
999 _c108733
_d108733