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Asymptotique de Born-Oppenheimer pour la prédissociation moléculaire (cas de potentiels réguliers)
Full text linkOn the generalized Kato spectrum
Full text link2010 Mathematics Subject Classification: 47A10.We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory
Structure of the Spectra and Resonances of Schrödinger Operators
Full text linkThe main goal of this paper is to study the spectrum and resonances of several classes of Schrödinger operators. Two important examples occurring in mathematical physics are discussed: harmonic oscillator and Hamiltonian of hydrogen atom.
Keywords: Schrödinger operator, Spectrum, Periodic potential, Resonances
L2-boundedness and L2-compactness of a class of Fourier integral operators
No full textIn this paper, we study the L2-boundedness and L2-compactness of a class of Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).Mathematic
Left and right generalized Drazin invertible operators and local spectral theory
No full textIn this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if and only if admits a generalized Kato decomposition and has the SVEP at 0 (resp. it admits a generalized Kato decomposition and its adjoint has the SVEP at 0. In addition, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting finite rank perturbations. Furthermore, we investigate the transmission of some local spectral properties from a bounded linear operator, as the SVEP, Dunford property (C), and property (β), to its generalized Drazin invers
Asymptotic Analysis for Schrödinger Hamiltonians via Birkhoff-Gustavson Normal Form
No full text30 pagesThis article reviews the Birkhoff-Gustavson normal form theorem (BGNF) near an equilibrium point of a quantum Hamiltonian. The BGNF process is thereafter used to investigate the spectrum of Schrödinger operators in the 1:1, 1:2 and 1:3 resonances. A computer program is proposed to compute the coefficients of the BGNF up to any order
New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
No full textThe method of invariant embedding for the solutions of boundary value problems yields an equivalent formulation to the initial boundary value problems by a system of Riccati operator differential equations. A combined technique based on invariant embedding approach and Yosida regularization is proposed in this paper for solving abstract Riccati problems and Dirichlet problems for the Poisson equation over a circular domain. We exhibit, in polar coordinates, the associated Neumann to Dirichlet operator, somme concrete properties of this operator are given. It also comes that from the existence of a solution for the corresponding Riccati equation, the problem can be solved in appropriate Sobolev spaces
A class of generalized integral operators
No full textIn this paper, we introduce a class of generalized integral operators that includes Fourier integral operators. We establish some conditions on these operators such that they do not have bounded extension on . This permit us in particular to construct a class of Fourier integral operators with bounded symbols in and in \bigcap_{0<\rho <1}S_{\rho ,1}^{0}
(\mathbb{R}^{n}\times \mathbb{R}^{n}) which cannot be extended to bounded operators in .Mathematic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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