Lower bounds for the number of resonances in even dimensional potential scattering
type: Item
instance of: scholarly article
title: Lower bounds for the number of resonances in even dimensional potential scattering
zbMATH Open document ID: 0939.35133
author: Antonio Sá Barreto
published in: Journal of Functional Analysis
publication date: 2000-06-26T00:00:00Z
review text: Let \(V \in {\mathbb C}_0^\infty({\mathbb R}^n,{\mathbb R})\), \(n \geq 4,\) be even, \(P=-\Delta+V\) and \(\{\lambda_j \}\) are resonances of P with multiplicity \(M(\lambda_j)\). It is proved that \[ \sum_j {M(\lambda_j) \over {|\log|\lambda_j|+i \arg\lambda_j |} } = \infty. \] As a direct consequence of this result a lower bound for the number of resonances is obtained.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81U20
zbMATH DE Number: 1398383
zbMATH Keywords: resonances
zbMATH Keywords: multiplicity
zbMATH Keywords: lower bound
MaRDI profile type: Publication
OpenAlex ID: W2087015416
cites work: On the heat trace of schrödinger operators
cites work: Sharp condition on the decay of the potential for the absence of a zero-energy ground state of the Schrodinger equation
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Q3729471
cites work: Q3671563
cites work: A polynomial bound on the number of the scattering poles for a potential in even dimensional spaces IRn
cites work: Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\)
cites work: Q4876293
cites work: Q5531193
cites work: Q4849528
cites work: Q3658440
cites work: Existence of Resonances in Even Dimensional Potential Scattering
cites work: Existence of resonances in three dimensions
cites work: Existence of resonances in potential scattering
cites work: Q4185363
cites work: Large time behavior of the \(L^ p\) norm of Schrödinger semigroups
cites work: Resonant states and poles of the scattering matrix for perturbations of - \(\Delta\)
cites work: Q4482959
cites work: Sharp bounds on the number of scattering poles in even-dimensional spaces
cites work: Sharp Bounds on the Number of Scattering Poles in the Two Dimensional Case
cites work: Q4831515
cites work: Sharp polynomial bounds on the number of scattering poles
cites work: Q4310192
DOI: 10.1006/JFAN.1999.3438
description: scientific article; zbMATH DE number 1398383