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008 870501s1987 gw a b 001 0 eng
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100 1 $aWeidmann, Joachim.
245 10 $aSpectral theory of ordinary differential operators /$cJoachim Weidmann.
260 $aBerlin ;$aNew York :$bSpringer-Verlag,$c©1987.
300 $avi, 303 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aLecture notes in mathematics ;$v1258
504 $aIncludes bibliographical references (pages 295-300) and index.
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 SchrO⁸dinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
540 $aCurrent copyright fee: GBP19.00$c42\0.$5Uk
650 0 $aDifferential operators.
650 0 $aSpectral theory (Mathematics)
650 04 $alineáris operátorok
650 04 $aközönséges differenciáloperátorok
650 6 $aOpérateurs différentiels.
650 6 $aSpectre (Mathématiques)
650 7 $aDifferential operators.$2fast$0(OCoLC)fst00893496
650 7 $aSpectral theory (Mathematics)$2fast$0(OCoLC)fst01129072
650 7 $aDifferentialoperator$2gnd
650 7 $aGewöhnlicher Differentialoperator$2gnd
650 7 $aSpektraltheorie$2gnd
650 07 $aOperadors diferencials.$2lemac
650 07 $aTeoria espectral (Matemàtica)$2lemac
650 7 $aDifferential operators.$2nli
650 7 $aDifferential equations, Partial.$2nli
776 08 $iOnline version:$aWeidmann, Joachim.$tSpectral theory of ordinary differential operators.$dBerlin ; New York : Springer-Verlag, ©1987$w(OCoLC)622948201
830 0 $aLecture notes in mathematics (Springer-Verlag) ;$v1258.
856 41 $3Table of contents$uhttp://www.gbv.de/dms/hbz/toc/ht002936760.pdf
856 41 $3Table of contents$uhttp://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2291836&custom_att_2=simple_viewer
856 41 $uhttp://www.springerlink.com/openurl.asp?genre=issue&issn=0075-8434&volume=1258
856 42 $3Inhaltstext$uhttp://www.zentralblatt-math.org/zmath/en/search/?an=0647.47052
856 4 $3Cover$uhttp://swbplus.bsz-bw.de/bsz012832715cov.htm$v20110329100645
856 $31850-9999$uhttp://www.springer.com/gb/$xBLDSS
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