多区间线性哈密顿系统的GKN理论.pdf

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,GKNTheoryforLinearHamiltonianSystemswithaCountableNumberofIntervalsAbstractThespectrumofdifferentialoperatorsisrelatedtomangdisparateanddeeptopicsinmathematicsandphysics,includingquantummechanics,stabilityoffluidandbiolog-icalengineering.Thest

15、ructurestheypresenthavetheprofoundsignificanceofmathe-maticalmodels,Hence,researchingonthetheoryoflinearHamiltoniansystemsisoftheoreticalandpracticalsignificance.In1850s,Glazman,KreinandNaimarkfoundedafamoustheorynamedGKNtheory.ThistheorygivesanalgebraicisomorphismbetweenthesetofLagrangi

16、ancom-plexsympleticsubspacesandthesetofself-adjointoperatorsintheHilbertspace.TheoriginalGKNtheorywasconfinedtoreal-valuedquasi-differentialexpressionofsecondorder.EverittandZettlextendedtheGKNtheorytothequasi-differentialexpressionsofarbitraryorderwithacountablenumberofintervalsonthere