Second-Order Differential Operators in the Limit Circle Case
Keyword(s):
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by an analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators.
1985 ◽
Vol 1
(3)
◽
pp. 225-230
◽
1975 ◽
Vol 52
(1)
◽
pp. 242-242
◽
1991 ◽
Vol 432
(1886)
◽
pp. 367-390
◽
Keyword(s):
1972 ◽
Vol s2-4
(4)
◽
pp. 741-744
◽
2010 ◽
Vol 284
(2-3)
◽
pp. 342-354
◽
Keyword(s):
Keyword(s):
1945 ◽
Vol 12
(2)
◽
pp. 255-273
◽
1971 ◽
Vol s2-4
(2)
◽
pp. 245-256
◽