Essentially Isospectral Transformations and Their Applications
نویسنده
چکیده
We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of eigenvalues and norming constants, oscillation of eigenfunctions, regularized trace formulas, and inverse uniqueness and existence theorems.
منابع مشابه
Strictly Isospectral Multiple-well Potentials and Their Multiple-parameter Supersymmetric Zero Modes in Unbroken Susyqm
" Scholars will have to choose between being widely read and being peer-reviewed " , USACM This is quant-ph/99mmnnn at LANL electronic archives Within unbroken SUSYQM, I present a formal discussion of the multiple-parameter bosonic zero modes and corresponding isospectral multiple-well Schroedinger potentials obtained by means of the general Riccati solution. The supersymmetric procedures are a...
متن کاملFactorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
We study possible factorizations of supersymmetric (SUSY) transformations in the one-dimensional quantum mechanics into chains of elementary Darboux transformations with nonsingular coefficients. A classification of irreducible (almost) isospectral transformations and of related SUSY algebras is presented. The detailed analysis of SUSY algebras and isospectral operators is performed for the thi...
متن کاملLiouville Correspondences between Integrable Hierarchies
In this paper, we study explicit correspondences between the integrable Novikov and Sawada–Kotera hierarchies, and between the Degasperis–Procesi and Kaup–Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada–Kotera equations, and the isospectral problems of the Degasperis–Procesi and Kaup–Kupershmidt equations relate...
متن کاملA Generalization of Mielnik’s One-parameter Isospectrality in Unbroken Susyqm
Within unbroken SUSYQM and for zero factorization energy, I present an iterative generalization of Mielnik’s one-parameter strictly isospectral method which leads to multiple-parameter bosonic zero modes and corresponding isospectral multipleparameter Schroedinger potentials. The supersymmetric procedures are an interesting and fruitful extension of onedimensional quantum mechanics. For recent ...
متن کاملIsospectral Graph Transformations, Spectral Equivalence, and Global Stability of Dynamical Networks
Abstract. In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network’s adjacency matrix up to a set of eigenvalues known beforehand from its graph structure. This procedure can be used to establish new equivalence relations on the class of all weighted graphs (netwo...
متن کامل