具有正则型点的奇异微分算子的自共轭扩张.pdfVIP

The Self-adjoint Extensions of Singular Differential Operators with a Real Regularity Point1 1,2 1 1 Wang Aiping , Sun Jiong , Gao Pengfei 1 Deptment of Mathmatics, Inner Mongolia Hohhot University （010021 ） 2 Deptment of Mathmatics, Tianjin University of Science and Technology, Tianjin （300222 ） Email: masun@ , aiping@ Abstract This paper deals with the self-adjoint domains of a singular symmetric differential expression l( y) with middle deficiency indices, under the condition that Π(L ) ∩R ≠∅, where Π(L ) is the 0 0 regularity domain of the corresponding minimal operator L . Using the real parameter L2 -solutions of 0 the equation l( y) λ y with λ ∈Π(L ) ∩R , we obtain a complete analytic description of the 0 0 0 self-adjoint domains of l( y) by giving a new decomposition of the maximal operator domain DM . And the description is independent of the properties of l( y) at infinity. Because the spectrum of self-adjoint operators is real, the advantage of using real parameter λ is not only because it is, in 0 general, easier to find explicit solutions but, more importantly, it yields information about the spectrum.