Spectral Theory of Ordinary Differential Operators

Häftad, Engelska, 1987

Del 1258 i serien Lecture Notes in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1987-05-06
Mått:155 x 235 x 27 mm
Vikt:472 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:304
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540179023

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

Formally 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.