含实参数的奇异哈密顿系统的平方可积解与哈密顿算子的谱.pdf

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3、¢ëêÛÉM—îXÚ²•ŒÈ)†M—îŽfÌÁ‡©Ì‡ïÄ3«m(a;b)þ¹k¢ëê‚5ÛÉM—îXÚ,±9†ƒƒéA‚5M—îŽf̯K.‚5M—îXÚ•k˜‡ÛÉà:ž,béA‚5M—îŽfäk?¿º•êd+=d=d,…éu½2I(I•Rþ?¿m«m),¹ëêM—îXÚ‚5Ã'²•ŒÈ)‡ê•r().±e(J:(1)r()

4、XÚü‡à:Ñ•ÛÉà:ž,

5、^«m©••{,•aq•k˜‡ÛÉà:œ/ž(Ø.'…cµ‚5M—îXÚ;ÛÉà:;º•ê;²•ŒÈ);ŸÌ;ëYÌ.i•H“‰ŒÆa¬ÆØ©Real-parameterSquare-integrableSolutionsandtheSpectrumofSingularHamiltonianSystemsAbstractInthispaper,therelationbetweenthelinearlyindependentquare-integrablesolu-tionsofsingularHamil

6、toniansystemswithreal-parameterandspectralproblemhasbeenconsideredin(a;b).Inthecaseofonesingularpoint,wesupposethearbitrarydeciencyindexofthecorrespondingHamiltonianoperatorbyd+=d=d.Foraxed2I(IisanarbitraryopenintervalinR),letr()denotethenumberoflinearlyindependentsqua

7、re-integrablesolutionsoftheHamiltoniansystemwithreal-parameter.Weobtainthefollowingresults:(1)r()

8、anoperatorS,anditdoesn'tlieintheessentialspectrumofSunderanadditionalcondition.Inthecaseoftwosingularpoints,weobtainthesimilarresultsbythe/two-interval0theory.Keywords:LinearHamiltoniansystem;Singularpoint;Deciencyindex;Square-integrablesolutions;Essentialspectrum;Continuou

9、sspectrum.ii•H“‰ŒÆa¬ÆØ©8¹1˜ÙÚó.............................................