TY - JOUR

T1 - On the Similarity of Some Differential Operators to Self-Adjoint Ones

AU - Faddeev, M. M.

AU - Shterenberg, R. G.

PY - 2002

Y1 - 2002

N2 - The paper is devoted to the study of the similarity to self-adjoint operators of operators of the form L=−sign x|x|αp(x)d2dx2, α>−1 , in the space L2(R) with weight |x|αp(x) . As is well known, the answer to this problem in the case p(x)≡1 is positive; it was obtained by using delicate methods of the theory of Hilbert spaces with indefinite metric. The use of a general similarity criterion in combination with methods of perturbation theory for differential operators allows us to generalize this result to a much wider class of weight functions p(x) .

AB - The paper is devoted to the study of the similarity to self-adjoint operators of operators of the form L=−sign x|x|αp(x)d2dx2, α>−1 , in the space L2(R) with weight |x|αp(x) . As is well known, the answer to this problem in the case p(x)≡1 is positive; it was obtained by using delicate methods of the theory of Hilbert spaces with indefinite metric. The use of a general similarity criterion in combination with methods of perturbation theory for differential operators allows us to generalize this result to a much wider class of weight functions p(x) .

U2 - 10.1023/A:1019810314450

DO - 10.1023/A:1019810314450

M3 - Article

VL - 72

SP - 261

EP - 270

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 2

ER -