000			03988nam a22004575i 4500
001			978-3-540-47912-3
003			DE-He213
005			20160624101828.0
007			cr nn 008mamaa
008			121227s1987 gw | s |||| 0|eng d
020			_a9783540479123 _9978-3-540-47912-3
024	7		_a10.1007/BFb0077960 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aWeidmann, Joachim. _eauthor.
245	1	0	_aSpectral Theory of Ordinary Differential Operators _h[electronic resource] / _cby Joachim Weidmann.
260		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c1987.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c1987.
300			_aVIII, 304 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v1258
505	0		_aFormally self-adjoint differential expressions -- Appendix to section 1: The separation of the Dirac operator -- Fundamental properties and general assumptions -- Appendix to section 2: Proof of the Lagrange identity for n>2 -- The minimal operator and the maximal operator -- Deficiency indices and self-adjoint extensions of T0 -- The solutions of the inhomogeneous differential equation (?-?)u=f; Weyl's alternative -- Limit point-limit circle criteria -- Appendix to section 6: Semi-boundedness of Sturm-Liouville type operators -- The resolvents of self-adjoint extensions of T0 -- The spectral representation of self-adjoint extensions of T0 -- Computation of the spectral matrix ? -- Special properties of the spectral representation, spectral multiplicities -- L2-solutions and essential spectrum -- Differential operators with periodic coefficients -- Appendix to section 12: Operators with periodic coefficients on the half-line -- Oscillation theory for regular Sturm-Liouville operators -- Oscillation theory for singular Sturm-Liouville operators -- Essential spectrum and absolutely continuous spectrum of Sturm-Liouville operators -- Oscillation theory for Dirac systems, essential spectrum and absolutely continuous spectrum -- Some explicitly solvable problems.
520			_aThese notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540179023
786			_dSpringer
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v1258
856	4	0	_uhttp://dx.doi.org/10.1007/BFb0077960
942			_2EBK1641 _cEBK
999			_c30935 _d30935