The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Abdelkader Intissar - One of the best experts on this subject based on the ideXlab platform.
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Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation
Transport Theory and Statistical Physics, 2009Co-Authors: Salma Charfi, Abdelkader Intissar, Aref JeribiAbstract:This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its Generalized Eigenvectors, and we assert its differentiability.
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On an Riesz basis of Generalized Eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid
Journal of Mathematical Analysis and Applications, 2004Co-Authors: Aref Jeribi, Abdelkader IntissarAbstract:Abstract In this paper we prove that the system of Generalized Eigenvectors of the operator (I+eK)−1d4/dx4 forms a Riesz basis of L2(]−L,L[) where K is the integral operator with kernel the Hankel function of the first kind and order 0. This operator was introduced in J. Sound Vibration 177 (1994) 259–275. We give positive answers to the hypotheses posed in that article.
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on an unconditional basis of Generalized Eigenvectors of the nonself adjoint gribov operator in bargmann space
Journal of Mathematical Analysis and Applications, 1999Co-Authors: Marietherese Aimar, Abdelkader Intissar, Aref JeribiAbstract:Abstract In this article we prove that the system of Generalized Eigenvectors of the Gribov operator is an unconditional basis in Bargmann space. We also give a Generalized diagonalization (in the Abel sense) of the semigroups, respectively, associated to this operator and to its square root. Finally, some open problems are pointed out.
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ANALYSE DE SCATTERING D'UN OPERATEUR CUBIQUE DE HEUN DANS L'ESPACE DE BARGMANN
Communications in Mathematical Physics, 1998Co-Authors: Abdelkader IntissarAbstract:The boundary conditions at infinity are used in a description of all maximal dissipative extensions in Bargmann space of the minimal Heun's operator \(\). The characteristic functions of the dissipative extensions are computed. Completeness theorems are obtained for the system of Generalized Eigenvectors.
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Criteria of denseness of Generalized Eigenvectors of a class of compact nonselfadjoint (or compact resolvant) operators and applications
Publications of the Research Institute for Mathematical Sciences, 1996Co-Authors: Marietherese Aimar, Abdelkader Intissar, Jean Martin PaoliAbstract:In this work we establish sufficient conditions on the denseness of the Generalized Eigenvectors for a class of compact (or compact resolvent) non self adjoint operators. We can apply our results to operators arising in many fields, particularly in field's theory and in abstract second order differential equations. Our results generalize some results of Aimar and al [1] and [2], Macaev and Keldysh [11] and Dunford-Schwartz [9],
Aref Jeribi - One of the best experts on this subject based on the ideXlab platform.
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on a riesz basis of finite dimensional invariant subspaces and application to gribov operator in bargmann space
Linear & Multilinear Algebra, 2013Co-Authors: Salma Charfi, Alaeddine Damergi, Aref JeribiAbstract:AbstractIn this paper, we are mainly concerned with a new class of unbounded perturbations of unbounded normal operators. We give a description of the changed spectrum and we establish different conditions in terms of the spectrum to prove the existence of Riesz basis of finite-dimensional invariant subspaces of Generalized Eigenvectors. The obtained results are of importance for application to a non-self-adjoint Gribov operator in Bargmann space.
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On an unconditional basis of Generalized Eigenvectors of an analytic operator and application to a problem of radiation of a vibrating structure in a light fluid
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Ines Feki, Aref Jeribi, Ridha SfaxiAbstract:Abstract In this paper, we prove that the system of Generalized Eigenvectors of the perturbed operator T ( e ) : = T 0 + e T 1 + e 2 T 2 + ⋯ + e k T k + ⋯ , forms an unconditional basis with parentheses in a separable Hilbert space X; where e ∈ C , T 0 is a closed densely defined linear operator on X with domain D ( T 0 ) , having compact resolvent, while T 1 , T 2 , … are linear operators on X, with the same domain D ⊃ D ( T 0 ) , satisfying a specific growing inequality. An application to a problem of radiation of a vibrating structure in a light fluid is presented.
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Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation
Transport Theory and Statistical Physics, 2009Co-Authors: Salma Charfi, Abdelkader Intissar, Aref JeribiAbstract:This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its Generalized Eigenvectors, and we assert its differentiability.
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On an Riesz basis of Generalized Eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid
Journal of Mathematical Analysis and Applications, 2004Co-Authors: Aref Jeribi, Abdelkader IntissarAbstract:Abstract In this paper we prove that the system of Generalized Eigenvectors of the operator (I+eK)−1d4/dx4 forms a Riesz basis of L2(]−L,L[) where K is the integral operator with kernel the Hankel function of the first kind and order 0. This operator was introduced in J. Sound Vibration 177 (1994) 259–275. We give positive answers to the hypotheses posed in that article.
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on an unconditional basis of Generalized Eigenvectors of the nonself adjoint gribov operator in bargmann space
Journal of Mathematical Analysis and Applications, 1999Co-Authors: Marietherese Aimar, Abdelkader Intissar, Aref JeribiAbstract:Abstract In this article we prove that the system of Generalized Eigenvectors of the Gribov operator is an unconditional basis in Bargmann space. We also give a Generalized diagonalization (in the Abel sense) of the semigroups, respectively, associated to this operator and to its square root. Finally, some open problems are pointed out.
Martin Haardt - One of the best experts on this subject based on the ideXlab platform.
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sum rate maximization in two way relaying systems with mimo amplify and forward relays via Generalized Eigenvectors
European Signal Processing Conference, 2010Co-Authors: Florian Roemer, Martin HaardtAbstract:In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming that the terminals have perfect channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user channels by subtracting the self-interference at the terminals. We derive the relay amplification matrix which maximizes the (weighted) sum rate in the case where the terminals have a single antenna. By algebraic manipulation of the rate expressions we can rewrite the optimization problem as a Generalized eigenvalue expression which depends on two real-valued parameters. The optimum is then found by a 2-D exhaustive search, which can be efficiently implemented via the bisection method. The resulting method is called RAGES (RAte-maximization via Generalized Eigenvectors for Single-antenna terminals). Moreover, both parameters have a physical interpretation which allows to find sub-optimal heuristics to reduce the complexity of the search even further. As shown in simulations, a corresponding suboptimal 1-D search is very close to the optimum sum rate.
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EUSIPCO - Sum-rate maximization in two-way relaying systems with MIMO amplify and forward relays via Generalized Eigenvectors
2010Co-Authors: Florian Roemer, Martin HaardtAbstract:In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming that the terminals have perfect channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user channels by subtracting the self-interference at the terminals. We derive the relay amplification matrix which maximizes the (weighted) sum rate in the case where the terminals have a single antenna. By algebraic manipulation of the rate expressions we can rewrite the optimization problem as a Generalized eigenvalue expression which depends on two real-valued parameters. The optimum is then found by a 2-D exhaustive search, which can be efficiently implemented via the bisection method. The resulting method is called RAGES (RAte-maximization via Generalized Eigenvectors for Single-antenna terminals). Moreover, both parameters have a physical interpretation which allows to find sub-optimal heuristics to reduce the complexity of the search even further. As shown in simulations, a corresponding suboptimal 1-D search is very close to the optimum sum rate.
Serguei Naboko - One of the best experts on this subject based on the ideXlab platform.
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green matrix estimates of block jacobi matrices i unbounded gap in the essential spectrum
Integral Equations and Operator Theory, 2018Co-Authors: Jan Janas, Serguei Naboko, Luis O. SilvaAbstract:This work deals with decay bounds for Green matrices and Generalized Eigenvectors of block Jacobi matrices when the real part of the spectral parameter lies in an infinite gap of the operator’s essential spectrum. We consider the cases of commutative and noncommutative matrix entries separately. An example of a block Jacobi operator with noncommutative entries and nonnegative essential spectrum is given to illustrate the results.
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ESTIMATES OF Generalized Eigenvectors OF HERMITIAN JACOBI MATRICES WITH A GAP IN THE ESSENTIAL SPECTRUM
Mathematika, 2012Co-Authors: Jan Janas, Serguei NabokoAbstract:In this paper we prove sharp estimates for Generalized Eigenvectors of Hermitian Jacobi matrices associated with the spectral parameter lying in a gap of their essential spectra. The estimates do not depend on the main diagonals of these matrices. The types of estimates obtained for bounded and unbounded gaps are different. These estimates extend the previous ones found in [J. Janas, S. Naboko and G. Stolz, Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices. Int. Math. Res. Not. 4 (2009), 736–764], for the spectral parameter being outside the whole spectrum of Jacobi matrices. Examples illustrating optimality of our results are also given.
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Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis
Journal of Approximation Theory, 2009Co-Authors: Serguei Naboko, Irina Pchelintseva, Luis O. SilvaAbstract:For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end, we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the Generalized Eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.
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Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging
Differential Operators and Related Topics, 2000Co-Authors: Jan Janas, Serguei NabokoAbstract:We consider unbounded, selfadjoint Jacobi matrices with weights λ n = n α(1+Δ n ), LimΔ n =0 and α \(\alpha \in (\frac{1} {2},1)\). The asymptotics for Generalized Eigenvectors of fixed energy is obtained. This allows to carry out, by using so called grouping in block method, analysis of absolutely continuous spectra of our class of operators. The main role play here algebraic properties of Pauli matrices arising in natural way in the analysis of corresponding transfer matrices. It happenes that the commutation relations between Pauli matrices lead to the appearance of Cesaro-like averages in our study.
Florian Roemer - One of the best experts on this subject based on the ideXlab platform.
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sum rate maximization in two way relaying systems with mimo amplify and forward relays via Generalized Eigenvectors
European Signal Processing Conference, 2010Co-Authors: Florian Roemer, Martin HaardtAbstract:In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming that the terminals have perfect channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user channels by subtracting the self-interference at the terminals. We derive the relay amplification matrix which maximizes the (weighted) sum rate in the case where the terminals have a single antenna. By algebraic manipulation of the rate expressions we can rewrite the optimization problem as a Generalized eigenvalue expression which depends on two real-valued parameters. The optimum is then found by a 2-D exhaustive search, which can be efficiently implemented via the bisection method. The resulting method is called RAGES (RAte-maximization via Generalized Eigenvectors for Single-antenna terminals). Moreover, both parameters have a physical interpretation which allows to find sub-optimal heuristics to reduce the complexity of the search even further. As shown in simulations, a corresponding suboptimal 1-D search is very close to the optimum sum rate.
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EUSIPCO - Sum-rate maximization in two-way relaying systems with MIMO amplify and forward relays via Generalized Eigenvectors
2010Co-Authors: Florian Roemer, Martin HaardtAbstract:In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. Assuming that the terminals have perfect channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user channels by subtracting the self-interference at the terminals. We derive the relay amplification matrix which maximizes the (weighted) sum rate in the case where the terminals have a single antenna. By algebraic manipulation of the rate expressions we can rewrite the optimization problem as a Generalized eigenvalue expression which depends on two real-valued parameters. The optimum is then found by a 2-D exhaustive search, which can be efficiently implemented via the bisection method. The resulting method is called RAGES (RAte-maximization via Generalized Eigenvectors for Single-antenna terminals). Moreover, both parameters have a physical interpretation which allows to find sub-optimal heuristics to reduce the complexity of the search even further. As shown in simulations, a corresponding suboptimal 1-D search is very close to the optimum sum rate.
