000			03600nam a22005655i 4500
001			978-0-8176-4439-0
003			DE-He213
005			20161121230929.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780817644390 _9978-0-8176-4439-0
024	7		_a10.1007/0-8176-4439-3 _2doi
050		4	_aQA404.7-405
072		7	_aPBWL _2bicssc
072		7	_aMAT033000 _2bisacsh
082	0	4	_a515.96 _223
100	1		_aDemuth, Michael. _eauthor.
245	1	0	_aDetermining Spectra in Quantum Theory _h[electronic resource] / _cby Michael Demuth, Maddaly Krishna.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2005.
300			_aX, 219 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Mathematical Physics ; _v44
505	0		_aMeasures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications.
520			_aThemainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di?erent journals. We collected them, added some and gave some overview that can serve as a platform for further research activities. Spectral theory of Schr¨ odinger type operators has a long history; however the most widely used methods were limited in number. For any selfadjoint operatorA on a separable Hilbert space the spectrum is identi?ed by looking atthetotalspectralmeasureassociatedwithit;oftenstudyingsuchameasure meant looking at some transform of the measure. The transforms were of the form f,?(A)f which is expressible, by the spectral theorem, as ?(x)dµ (x) for some ?nite measureµ . The two most widely used functions? were the sx ?1 exponential function?(x)=e and the inverse function?(x)=(x?z) . These functions are “usable” in the sense that they can be manipulated with respect to addition of operators, which is what one considers most often in the spectral theory of Schr¨ odinger type operators. Starting with this basic structure we look at the transforms of measures from which we can recover the measures and their components in Chapter 1. In Chapter 2 we repeat the standard spectral theory of selfadjoint op- ators. The spectral theorem is given also in the Hahn–Hellinger form. Both Chapter 1 and Chapter 2 also serve to introduce a series of de?nitions and notations, as they prepare the background which is necessary for the criteria in Chapter 3.
650		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aOperator theory.
650		0	_aPartial differential equations.
650		0	_aPotential theory (Mathematics).
650		0	_aPhysics.
650		0	_aQuantum physics.
650	1	4	_aMathematics.
650	2	4	_aPotential Theory.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aQuantum Physics.
650	2	4	_aPartial Differential Equations.
650	2	4	_aOperator Theory.
650	2	4	_aFunctional Analysis.
700	1		_aKrishna, Maddaly. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643669
830		0	_aProgress in Mathematical Physics ; _v44
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4439-3
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506053 _d506053