共查询到10条相似文献,搜索用时 78 毫秒
1.
Jussi Behrndt 《Journal of Mathematical Analysis and Applications》2007,334(2):1439-1449
We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator. 相似文献
2.
研究一类带不定权函数的奇型Sturm-Liouville算子,给出相应自伴算子在无穷点邻域的局部可定性. 相似文献
3.
In this paper we develop a perturbation approach to investigate spectral problems for singular ordinary differential operators with indefinite weight functions. We prove a general perturbation result on the local spectral properties of selfadjoint operators in Krein spaces which differ only by finitely many dimensions from the orthogonal sum of a fundamentally reducible operator and an operator with finitely many negative squares. This result is applied to singular indefinite Sturm-Liouville operators and higher order singular ordinary differential operators with indefinite weight functions. 相似文献
4.
Stephan Ramon Garcia Mihai Putinar 《Transactions of the American Mathematical Society》2006,358(3):1285-1315
We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.
5.
We consider a class of boundary value problems for Sturm-Liouville operators with indefinite weight functions. The spectral parameter appears nonlinearly in the boundary condition in the form of a function τ which has the property that λ?λτ(λ) is a generalized Nevanlinna function. We construct linearizations of these boundary value problems and study their spectral properties. 相似文献
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7.
The stability of various factorizations of self-adjoint rational matrix functions and matrix polynomials, as well as of hermitian solutions of symmetric matrix algebraic Riccati equations, is studied. In the first part of this paper results on stability of certain classes of invariant subspaces of a matrix which is self-adjoint in an indefinite inner product were obtained. These results serve as the main tools in the investigation. 相似文献
8.
We study eigenvalue problems Fy = λ Gy consisting of Hamiltonian systems of ordinary differential equations on a compact interval with symmetric λ-linear boundary conditions. The problems we are interested in are non-definite: neither left-nor right-definite. Instead of this, we give some weak condition on one coefficient of the Hamiltonian system which ensures that a hermitian form associated with the operator F has at most finitely many negative squares. This enables us to study the problem by the help of a compact self-adjoint operator in a Pontrjagin space and we obtain as a main result uniformly convergent eigenfunction expansions. In the final section, applications to formally self-adjoint differential equations of higher order are given. 相似文献
9.
For a semibounded below self-adjoint operatorA in a Hilbert spaceH and a singular operatorV acting in theA-scale of Hilbert spaces, the notion of generalized sumA?V is introduced. Conditions are found forA?V to be self-adjoint in ?. In particular, it is shown that if a symmetric operatorV is semibounded or has a spectral gap, then there exists an α such that the generalized sumA?αV is a self-adjoint operator inH. For a symmetric restrictionA = A‖D, D C D(A), with deficiency indices (1, 1), it is proved that each self-adjoint extension à of A admits representation as a generalized sum Ã=A?V. 相似文献