منابع مشابه
Compactness of Isospectral Potentials
The Schrödinger operator −∆+V , of a compact Riemannian manifold M , has pure point spectrum. Suppose that V0 is a smooth reference potential. Various criteria are given which guarantee the compactness of all V satisfying spec(−∆+V ) = spec(−∆+V0). In particular, compactness is proved assuming an a priori bound on the Ws,2(M) norm of V , where s > n/2 − 2 and n = dimM . This improves earlier wo...
متن کاملCompactness of isospectral sets
© Séminaire de Théorie spectrale et géométrie (Grenoble), 1991, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi...
متن کاملHeat Trace Asymptotics and Compactness of Isospectral Potentials for the Dirichlet Laplacian
Let Ω be a C∞-smooth bounded domain of R, n ≥ 1, and let the matrix a ∈ C(Ω;R 2 ) be symmetric and uniformly elliptic. We consider the L(Ω)-realization A of the operator −div(a∇·) with Dirichlet boundary conditions. We perturb A by some real valued potential V ∈ C∞ 0 (Ω) and note AV = A + V . We compute the asymptotic expansion of tr ( eV − e ) as t ↓ 0 for any matrix a whose coefficients are h...
متن کاملIsospectral Potentials and Darboux Transformations
allowed for determined boundary conditions corresponding to the standard potential . With the very useful Darboux transformation (DT) [3-6] is possible to generalize any specific standard potential and thus generate new interaction models with the same energy levels. The DT is related to the Sturm-Liouville theory [7-10], and it is easy to see the implicit presence of DT in supersymmetric quant...
متن کاملStrictly Isospectral Susy Potentials and the Riccati Superposition Principle
Generating quasi-isospectral potentials by the methods of supersymmetric quantum mechanics (SUSYQM) is a simple and well-known mathematical technique [1]. Its relationships with intertwining, factorization, Darboux covariance, and inverse scattering procedures have been recently reviewed by the author [2]. Also, the author, either in collaboration or alone [3] dealt extensively with a SUSYQM pr...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03813-9