The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Nikolai Dokuchaev - One of the best experts on this subject based on the ideXlab platform.
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on linear weak predictability with single Point Spectrum degeneracy
arXiv: Information Theory, 2017Co-Authors: Nikolai DokuchaevAbstract:The paper studies properties of continuous time processes with Spectrum degeneracy at a single Point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense, meaning that convolution integrals over future times can be approximated by causal convolutions over past times. The corresponding predicting kernels are time invariant, and they are presented explicitly in the frequency domain via their transfer functions. These predictors are "universal" meaning that they do not require to know details of the Spectrum of the underlying processes; the same predictor can be used for the entire class of processes with a single Point Spectrum degeneracy. The predictors feature some robustness with respect to noise contamination.
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On linear weak predictability with single Point Spectrum degeneracy
Applied and Computational Harmonic Analysis, 1Co-Authors: Nikolai DokuchaevAbstract:Abstract The paper studies predicting problems for continuous time signals with the Fourier transforms vanishing with a certain rate at a single Point. It shows that, with some linear causal predictors, anticausal convolution integrals over future times for these processes can be approximated by causal convolutions over past times. The corresponding predicting kernels are time invariant, and they are presented explicitly in the frequency domain via their transfer functions. These predictors are “universal” meaning that they do not require to know details of the Spectrum of the underlying signals; the same predictor can be used for the entire class of signals with a single Point Spectrum degeneracy. The predictors feature some robustness with respect to noise contamination.
John Jasper - One of the best experts on this subject based on the ideXlab platform.
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the schur horn theorem for operators with three Point Spectrum
Journal of Functional Analysis, 2013Co-Authors: John JasperAbstract:Abstract We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three Points in the Spectrum. Our result gives a Schur–Horn theorem for operators with three Point Spectrum analogous to Kadisonʼs Pythagorean theorem and carpenterʼs theorem, which characterize the diagonals of orthogonal projections.
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The Schur–Horn theorem for operators with three Point Spectrum
Journal of Functional Analysis, 2013Co-Authors: John JasperAbstract:Abstract We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three Points in the Spectrum. Our result gives a Schur–Horn theorem for operators with three Point Spectrum analogous to Kadisonʼs Pythagorean theorem and carpenterʼs theorem, which characterize the diagonals of orthogonal projections.
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The Schur-Horn theorem for operators with three Point Spectrum
arXiv: Functional Analysis, 2010Co-Authors: John JasperAbstract:We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three Points in the Spectrum. Our result gives a Schur-Horn theorem for operators with three Point Spectrum analogous to Kadison's result for orthogonal projections.
César R. De Oliveira - One of the best experts on this subject based on the ideXlab platform.
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Persistence of Point Spectrum for Perturbations of One-Dimensional Operators with Discrete Spectra
Spectral Theory and Mathematical Physics, 2020Co-Authors: César R. De Oliveira, Mariane PigossiAbstract:Sufficient conditions are given, for the preservation of the pure Point Spectrum, as well as dynamical localization properties, of autonomous and time-periodic perturbations of self-adjoint operators in Open image in new window with simple pure Point spectra whose eigenvalues have no accumulation Point.
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Quantum quasiballistic dynamics and thick Point Spectrum.
Letters in Mathematical Physics, 2019Co-Authors: Moacir Aloisio, Silas L. Carvalho, César R. De OliveiraAbstract:We obtain dynamical lower bounds for some self-adjoint operators with pure Point Spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick Point Spectrum, typically in Baire's sense, the dynamics of each initial condition (with respect to some orthonormal bases of the space) presents a quasiballistic behaviour. We present explicit applications to some Schrodinger operators.
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Point Spectrum and SULE for Time-Periodic Perturbations of Discrete 1D Schrödinger Operators with Electric Fields
Journal of Statistical Physics, 2018Co-Authors: César R. De Oliveira, Mariane PigossiAbstract:We use the KAM technique to present a proof of pure Point Spectrum for the quasi-energy operator and a version of the SULE condition for suitable small time-periodic perturbations of discrete one-dimensional Schrodinger operators with uniform electric fields.
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A Floquet Operator with Purely Point Spectrum and Energy Instability
Annales Henri Poincaré, 2007Co-Authors: César R. De Oliveira, Mariza Stefanello SimsenAbstract:An example of Floquet operator with purely Point Spectrum and energy instability is presented. In the unperturbed energy eigenbasis its eigenfunctions are exponentially localized.
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A Floquet Operator with Pure Point Spectrum and Energy Instability
arXiv: Mathematical Physics, 2007Co-Authors: César R. De Oliveira, Mariza Stefanello SimsenAbstract:An example of Floquet operator with purely Point Spectrum and energy instability is presented. In the unperturbed energy eigenbasis its eigenfunctions are exponentially localized.
Efim Dinaburg - One of the best experts on this subject based on the ideXlab platform.
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Methods of KAM-theory for long-range quasi-periodic operators on ${\bf Z}^\nu$. Pure Point Spectrum
Communications in Mathematical Physics, 1993Co-Authors: V. A. Chulaevsky, Efim DinaburgAbstract:We consider the class of quasi-periodic self-adjoint operatorsĤ(x)) = $$\hat D(x) + \hat V(x)$$ ,x∈S 1=ℝ1/ℤ1, on a multi-dimensional lattice ℤ v , with the matrix elements $$\hat D_{mn} (x) = \delta _{mn} D(x + n\omega ), \hat V_{mn} (x) = V(m - n, x + n\omega )$$ , whereD(x+1) =D(x), V(n, s+1) =V(n, x), ω ∈ ℝ v and |V(n, x)| ≤ ee −r|n|,r > 0. We prove that, if e is small enough,V(n,·) andD(·) satisfy some conditions of smoothness, andD(·) is non-degenerate, then for a.e. ω and for a.e.x∈S 1 the operatorĤ(x) has pure Point Spectrum. All its eigenfunctions belong tol 1(ℤ v ).
M. Vittot - One of the best experts on this subject based on the ideXlab platform.
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weakly regular floquet hamiltonians with pure Point Spectrum
Reviews in Mathematical Physics, 2002Co-Authors: Pierre Duclos, O. Lev, P. Šťovíček, M. VittotAbstract:We study the Floquet Hamiltonian -i∂t + H + V(ωt), acting in L2([0,T],ℋ, dt), as depending on the parameter ω = 2π/T. We assume that the Spectrum of H in ℋ is discrete, , but possibly degenerate, and that t ↦ V(t) ∈ ℬ(ℋ) is a 2π-periodic function with values in the space of Hermitian operators on ℋ. Let J > 0 and set . Suppose that for some σ > 0 it holds true that ∑hm > hnMmMn (hm - hn)-σ < ∞ where Mm is the multiplicity of hm. We show that in that case there exist a suitable norm to measure the regularity of V, denoted ∊V, and positive constants, ∊⋆ and δ⋆, with the property: if ∊V < ∊⋆ then there exists a measurable subset Ω∞ ⊂ Ω0 such that its Lebesgue measure fulfills |Ω∞| ≥ |Ω0| - δ⋆ ∊V and the Floquet Hamiltonian has a pure Point Spectrum for all ω∈Ω∞.
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Weakly Regular Floquet Hamiltonians with Pure Point Spectrum
Reviews in Mathematical Physics, 2002Co-Authors: Pierre Duclos, O. Lev, P. Šťovíček, M. VittotAbstract:We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on the parameter omega. We assume that the Spectrum of H is discrete, {h_m (m = 1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m - h_n)^(-sigma) |Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure Point Spectrum for all omega in Omega_infinity.
