کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642973 | 1341362 | 2007 | 15 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Alternative approaches to asymptotic behaviour of eigenvalues of some unbounded Jacobi matrices Alternative approaches to asymptotic behaviour of eigenvalues of some unbounded Jacobi matrices](/preview/png/4642973.png)
In this article we calculate the asymptotic behaviour of the point spectrum for some special self-adjoint unbounded Jacobi operators J acting in the Hilbert space l2=l2(N)l2=l2(N). For given sequences of positive numbers λnλn and real qnqn the Jacobi operator is given by J=SW+WS*+QJ=SW+WS*+Q, where Q=diag(qn)Q=diag(qn) and W=diag(λn)W=diag(λn) are diagonal operators, S is the shift operator and the operator J acts on the maximal domain. We consider a few types of the sequences {qn}{qn} and {λn}{λn} and present three different approaches to the problem of the asymptotics of eigenvalues of various classes of J's. In the first approach to asymptotic behaviour of eigenvalues we use a method called successive diagonalization, the second approach is based on analytical models that can be found for some special J's and the third method is based on an abstract theorem of Rozenbljum.
Journal: Journal of Computational and Applied Mathematics - Volume 200, Issue 1, 1 March 2007, Pages 342–356