Limit points of eigenvalues of truncated tridiagonal operators
[摘要] Let T be the tridiagonal operator Te-n = a(n)e(n+1) + a(n-1)e(n-1) + b(n)e(n), Te-1 = a(1)e(2) + b(1)e(1), acting on a fixed orthonormal basis {e(n)}, n = 1,2,..., of a Hilbert space H. Let P-N be the orthogonal projection on the finite-dimensional space H-N spanned by the elements {e(1), e(2),...,e(N)} and let T-N be the truncated operator T-N = PNTPN. If T has a unique self-adjoint extension then the set Lambda (T) = {lambda: there exists a sequence of eigenvalues lambda (N) of T-N with the property lambda (N) --> lambda} contains the spectrum sigma (T) of T and examples show that, in general, sigma (T) not equal Lambda (T). For many reasons, the knowledge of the equality sigma (T) = Lambda (T) is important. In this paper sufficient conditions are presented such that sigma (T) = Lambda (T). (C) 2001 Elsevier Science B.V. All rights reserved.
[发布日期] 2001-08-01 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] tridiagonal operators;spectrum of tridiagonal operators;limit points of eigenvalues of truncated tridiagonal operators;orthogonal polynomials;continued fractions [时效性]
