On the asymptotics of scattering phases for the Schrödinger equation
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D. R. Yafaev (1990)
Annales de l'I.H.P. Physique théorique
Leonid Parnovski, Alexander V. Sobolev (2000)
Journées équations aux dérivées partielles
We consider the operator in , of the form with a function periodic with respect to a lattice in . We prove that the number of gaps in the spectrum of is finite if . Previously the finiteness of the number of gaps was known for . Various approaches to this problem are discussed.
Dias, João-Paulo, Figueira, Mário (1982)
Portugaliae mathematica
Yiming Long (1989)
Annales de l'I.H.P. Analyse non linéaire
Mohamed Ben Chrouda (2016)
Annales Polonici Mathematici
This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian as well as the hypoellipticity of on noninvariant open sets.
Bao-Zhu Guo, Jun-Min Wang, Cui-Lian Zhou (2008)
ESAIM: Control, Optimisation and Calculus of Variations
We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...
Wiesław Cupała (1993)
Studia Mathematica
Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.
Abdoul Ifra, Lotfi Riahi (2004)
Annales Polonici Mathematici
We consider the general Schrödinger operator on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity considered by Zhao and Pinchover. As an application we study the cone of all positive L-solutions continuously vanishing...
Wiesław Cupała (1990)
Studia Mathematica
Hubert Kalf, Rainer Hempel, Andreas M. Hinz (1987)
Mathematische Annalen
Ian Knowles (1978)
Mathematische Annalen
Klaus-Jürgen Eckardt (1973/1974)
Manuscripta mathematica
Hiroshi Isozaki (1982)
Journal für die reine und angewandte Mathematik
Inahama, Yuzuru, Shirai, Shin-ichi (2006)
Mathematical Physics Electronic Journal [electronic only]
Sichun Wang (1997)
Studia Mathematica
For d > 1, let , , where f̂ is the Fourier transform of , and its maximal operator. P. Sjölin ([11]) has shown that for radial f, the estimate (*) holds for p = 4n/(2n-1) and fails for p > 4n/(2n-1). In this paper we show that for non-radial f, (*) fails for p > 2. A similar result is proved for a more general maximal operator.
Zasorin, Yuriy Valentinovich (2001)
Abstract and Applied Analysis
Anne Berthier (1982)
Annales scientifiques de l'École Normale Supérieure
Yu. Semenov (1979)
Studia Mathematica
D. R. Yafaev (1988/1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
A. V. Sobolev, D. R. Yafaev (1986)
Annales de l'I.H.P. Physique théorique