rellich’s theorem
Recently Published Documents


TOTAL DOCUMENTS

8
(FIVE YEARS 1)

H-INDEX

2
(FIVE YEARS 0)

2021 ◽  
pp. 2150015
Author(s):  
T. Adachi ◽  
K. Itakura ◽  
K. Ito ◽  
E. Skibsted

We develop a new scheme of proofs for spectral theory of the [Formula: see text]-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich’s theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich’s theorem which is unified with exponential decay estimates studied previously only for [Formula: see text]-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with ‘zeroth order’ operators. In particular, they do not rely on Mourre’s differential inequality technique.



2018 ◽  
Vol 291 (3-4) ◽  
pp. 1435-1449 ◽  
Author(s):  
Kyohei Itakura


2016 ◽  
Vol 28 (05) ◽  
pp. 1650010 ◽  
Author(s):  
K. Ito ◽  
E. Skibsted

We show an optimal version of Rellich’s theorem for generalized [Formula: see text]-body Schrödinger operators. It applies to singular potentials, in particular, to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof relies on a Mourre estimate [10] and a functional calculus localization technique.



1990 ◽  
Vol 145 (2) ◽  
pp. 516-523 ◽  
Author(s):  
Fernando Galaz Fontes






1969 ◽  
Vol 12 (2) ◽  
pp. 229-231
Author(s):  
Robert A. Adams

In a recent note [3] in this department C. Clark has shown that Rellich's theorem on the compactness of the imbedding is valid if G is the "spiny urchin" domain obtained by removing from the plane the union of the sets Sk (k = 1, 2,…) defined in polar coordinates by



1964 ◽  
Vol 7 (3) ◽  
pp. 435-440
Author(s):  
Colin Clark

Let G be a region in Eućlidean n-space En and consider the eigenvalue problem Δ2u = λu on G, with boundary conditions u = 0 on Γ, the boundary of G. (To be precise, we are considering the eigenvalue problem for the self-adjoint 2 realization L associated with the Laplacian -Δ2and zero boundary condition, acting in L2(G), cf Browder [2]). If G is bounded, the spectrum of this problem is discrete, but Rellich showed in 1952 [6] that the spectrum could also be discrete for certain unbounded regions which he introduced and called "infinitely narrow tubes".



Sign in / Sign up

Export Citation Format

Share Document