Eigenvalue Problems of Atkinson, Feller and Krein, and Their Mutual Relationship
نویسنده
چکیده
It is shown that every regular Krein-Feller eigenvalue problem can be transformed to a semidefinite Sturm-Liouville problem introduced by Atkinson. This makes it possible to transfer results between the corresponding theories. In particular, Prüfer angle methods become available for Krein-Feller problems.
منابع مشابه
The Krein signature, Krein eigenvalues, and the Krein Oscillation Theorem
In this paper the problem of locating eigenvalues of negative Krein signature is considered for operators of the form JL, where J is skew-symmetric with bounded inverse and L is self-adjoint. A finite-dimensional matrix, hereafter referred to as the Krein matrix, associated with the eigenvalue problem JLu = λu is constructed with the property that if the Krein matrix has a nontrivial kernel for...
متن کاملA Hamiltonian-Krein (instability) index theory for KdV-like eigenvalue problems
The Hamiltonian-Krein (instability) index is concerned with determining the number of eigenvalues with positive real part for the Hamiltonian eigenvalue problem JLu = λu, where J is skewsymmetric and L is self-adjoint. If J has a bounded inverse the index is well-established, and it is given by the number of negative eigenvalues of the operator L constrained to act on some finite-codimensional ...
متن کاملThe Krein Matrix and an Interlacing Theorem
Consider the linear general eigenvalue problem Ay = λBy , where A and B are both invertible and Hermitian N × N matrices. In this paper we construct a set of meromorphic functions, the Krein eigenvalues, whose zeros correspond to the real eigenvalues of the general eigenvalue problem. The Krein eigenvalues are generated by the Krein matrix, which is constructed through projections on the positi...
متن کاملNonlinear eigenvalue { eigenvector problems for STP matrices
A matrix A is said to be strictly totally positive (STP) if all its minors are strictly positive. STP matrices were independently introduced by Schoenberg in 1930 (see [13, 14]) and by Krein and Gantmacher in the 1930s. The main results concerning eigenvalues and eigenvectors of STP matrices were proved by Gantmacher and Krein in their 1937 paper [6]. (An announcement appeared in 1935 in [5]. C...
متن کاملEvolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow
Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005