摘要 : Let A(center dot) be a densely defined, closed, symmetric operator in the complex, separable Hilbert space 9-t with equal deficiency indices and denote by N-i = ker(((center dot)A)(& lowast; )- iI(H)), dim(Ni) = k is an element of... 展开 Let A(center dot) be a densely defined, closed, symmetric operator in the complex, separable Hilbert space 9-t with equal deficiency indices and denote by N-i = ker(((center dot)A)(& lowast; )- iI(H)), dim(Ni) = k is an element of N boolean OR {infinity}, the associated deficiency subspace of (center dot)A. If A denotes a self-adjoint extension of A(center dot) in 9-t, the Donoghue m-operator MDo A,N-i ( <middle dot> ) in N-i associated with the pair (A, N-i) is given by M-A,Ni( )Do(z) = zI(Ni )+ (z(2) + 1)P-Ni (A- zI(H))-1P(Ni) |N-i ,z is an element of C R, with INi the identity operator in Ni, and PNi the orthogonal projection in 9-t onto Ni. Assuming the standard local integrability hypotheses on the coefficients p, q, r, we study all self-adjoint realizations corresponding to the differential expression tau = 1/r(x) [- d/dx p(x) d/dx+q(x)] for a.e. x is an element of (a, b) subset of R, in L-2((a, b); rdx), and, as our principal aim in this paper, systematically construct the associated Donoghue m-functions (respectively, (2 x 2) matrices) in all cases where tau is in the limit circle case at least at one interval endpoint a or b. 收起