Littérature scientifique sur le sujet « H-Pseudodifferential operators »
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Articles de revues sur le sujet "H-Pseudodifferential operators"
Yang, Jie. « On L 2 -Boundedness of h -Pseudodifferential Operators ». Journal of Function Spaces 2021 (20 février 2021) : 1–5. http://dx.doi.org/10.1155/2021/6690963.
Texte intégralTaylor, Michael. « The Technique of Pseudodifferential Operators (H. O. Cordes) ». SIAM Review 38, no 3 (septembre 1996) : 540–42. http://dx.doi.org/10.1137/1038101.
Texte intégralDeng, Yu-long. « Commutators of Pseudodifferential Operators on Weighted Hardy Spaces ». Journal of Mathematics 2022 (20 janvier 2022) : 1–6. http://dx.doi.org/10.1155/2022/8851959.
Texte intégralHitrik, Michael, et Johannes Sjöstrand. « Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point ». Canadian Journal of Mathematics 60, no 3 (1 juin 2008) : 572–657. http://dx.doi.org/10.4153/cjm-2008-028-3.
Texte intégralRabinovich, V. S. « Local exponential estimates for h-pseudodifferential operators and tunneling for Schrödinger, Dirac, and square root Klein-Gordon operators ». Russian Journal of Mathematical Physics 16, no 2 (juin 2009) : 300–308. http://dx.doi.org/10.1134/s1061920809020149.
Texte intégralRabinovich, V. « Exponential estimates of solutions of pseudodifferential equations on the lattice $${(h \mathbb{Z})^{n}}$$ : applications to the lattice Schrödinger and Dirac operators ». Journal of Pseudo-Differential Operators and Applications 1, no 2 (10 mars 2010) : 233–53. http://dx.doi.org/10.1007/s11868-010-0005-2.
Texte intégralElong, Ouissam. « On the LP boundedness of h-Fourier integral operators with rough symbols ». Mathematica Montisnigri 54 (2022) : 25–39. http://dx.doi.org/10.20948/mathmontis-2022-54-3.
Texte intégralOrlov, A. Yu, et P. Winternitz. « P∞ Algebra of KP, Free Fermions and 2-Cocycle in the Lie Algebra of Pseudodifferential Operators ». International Journal of Modern Physics B 11, no 26n27 (30 octobre 1997) : 3159–93. http://dx.doi.org/10.1142/s0217979297001532.
Texte intégralRozendaal, Jan. « Rough Pseudodifferential Operators on Hardy Spaces for Fourier Integral Operators II ». Journal of Fourier Analysis and Applications 28, no 4 (13 juillet 2022). http://dx.doi.org/10.1007/s00041-022-09959-x.
Texte intégral« Partial parabolicity of the boundary-value problem for pseudodifferential equations in a layer ». V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no 89 (2019). http://dx.doi.org/10.26565//2221-5646-2019-89-03.
Texte intégralThèses sur le sujet "H-Pseudodifferential operators"
Schneider, Achim [Verfasser]. « H∞-calculus for cone pseudodifferential operators and the Dirichlet to Neumann map / Achim Schneider ». Hannover : Technische Informationsbibliothek (TIB), 2016. http://d-nb.info/1122663501/34.
Texte intégralZreik, Mahdi. « Spectral properties of Dirac operators on certain domains ». Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0085.
Texte intégralThis thesis mainly focused on the spectral analysis of perturbation models of the free Dirac operator, in 2-D and 3-D space.The first chapter of this thesis examines perturbation of the Dirac operator by a large mass M, supported on a domain. Our main objective is to establish, under the condition of sufficiently large mass M, the convergence of the perturbed operator, towards the Dirac operator with the MIT bag condition, in the norm resolvent sense. To this end, we introduce what we refer to the Poincaré-Steklov (PS) operators (as an analogue of the Dirichlet-to-Neumann operators for the Laplace operator) and analyze them from the microlocal point of view, in order to understand precisely the convergence rate of the resolvent. On one hand, we show that the PS operators fit into the framework of pseudodifferential operators and we determine their principal symbols. On the other hand, since we are mainly concerned with large masses, we treat our problem from the semiclassical point of view, where the semiclassical parameter is h = M^{-1}. Finally, by establishing a Krein formula relating the resolvent of the perturbed operator to that of the MIT bag operator, and using the pseudodifferential properties of the PS operators combined with the matrix structures of the principal symbols, we establish the required convergence with a convergence rate of mathcal{O}(M^{-1}).In the second chapter, we define a tubular neighborhood of the boundary of a given regular domain. We consider perturbation of the free Dirac operator by a large mass M, within this neighborhood of thickness varepsilon:=M^{-1}. Our primary objective is to study the convergence of the perturbed Dirac operator when M tends to +infty. Comparing with the first part, we get here two MIT bag limit operators, which act outside the boundary. It's worth noting that the decoupling of these two MIT bag operators can be considered as the confining version of the Lorentz scalar delta interaction of Dirac operator, supported on a closed surface. The methodology followed, as in the previous problem study the pseudodifferential properties of Poincaré-Steklov operators. However, the novelty in this problem lies in the control of these operators by tracking the dependence on the parameter varepsilon, and consequently, in the convergence as varepsilon goes to 0 and M goes to +infty. With these ingredients, we prove that the perturbed operator converges in the norm resolvent sense to the Dirac operator coupled with Lorentz scalar delta-shell interaction.In the third chapter, we investigate the generalization of an approximation of the three-dimensional Dirac operator coupled with a singular combination of electrostatic and Lorentz scalar delta-interactions supported on a closed surface, by a Dirac operator with a regular potential localized in a thin layer containing the surface. In the non-critical and non-confining cases, we show that the regular perturbed Dirac operator converges in the strong resolvent sense to the singular delta-interaction of the Dirac operator. Moreover, we deduce that the coupling constants of the limit operator depend nonlinearly on those of the potential under consideration.In the last chapter, our study focuses on the two-dimensional Dirac operator coupled with the electrostatic and Lorentz scalar delta-interactions. We treat in low regularity Sobolev spaces (H^{1/2}) the self-adjointness of certain realizations of these operators in various curve settings. The most important case in this chapter arises when the curves under consideration are curvilinear polygons, with smooth, differentiable edges and without cusps. Under certain conditions on the coupling constants, using the Fredholm property of certain boundary integral operators, and exploiting the explicit form of the Cauchy transform on non-smooth curves, we achieve the self-adjointness of the perturbed operator
Assal, Marouane. « Analyse spectrale des systèmes d'opérateurs h-pseudodifférentiels ». Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0586/document.
Texte intégralIn this work, we are interested in the spectral analysis of systems of semiclassical pseudodifferentialoperators. In the first part, we study the extension of the long time semiclassical Egorovtheorem in the case where the quantum Hamiltonian which generates the time evolution andthe initial quantum observable are two semiclassical pseudodifferential operators with matrixvaluedsymbols. Under an hyperbolicity condition on the principal symbol of the Hamiltonianwhich ensures the existence of the semiclassical projections, and for a class of observable thatare "semi-classically" block-diagonal with respect to these projections, we prove an Egorov theoremvalid in a large time interval of order log(h-1) known as the Ehrenfest time. Here h & 0is the semiclassical parameter.In the second part, we are interested in the spectral and scattering theories for self-adjointsystems of pseudodifferential operators. We develop a stationary approach for the study of thespectral shift function (SSF) associated to a pair of self-adjoint semiclassical Schrödinger operatorswith matrix-valued potentials. We prove a Weyl-type asymptotics with sharp remainderestimate on the SSF, and under the existence of a scalar escape function, a pointwise completeasymptotic expansion on its derivative. This last result is a generalisation in the matrix-valuedcase of a result of Robert and Tamura established in the scalar case near non-trapping energies.Our time-independent method allows us to treat certain potentials with energy-level crossings
Chapitres de livres sur le sujet "H-Pseudodifferential operators"
Helffer, Bernard. « h-Pseudodifferential Operators and Applications : An Introduction ». Dans Quasiclassical Methods, 1–49. New York, NY : Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1940-8_1.
Texte intégral« h-pseudodifferential operators ». Dans Spectral Asymptotics in the Semi-Classical Limit, 75–92. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511662195.008.
Texte intégralHelffer, B. « h-Pseudodifferential Operators and Applications ». Dans Encyclopedia of Mathematical Physics, 701–12. Elsevier, 2006. http://dx.doi.org/10.1016/b0-12-512666-2/00495-8.
Texte intégral« Pseudodifferential operators as smooth operators of L(H) ». Dans The Technique of Pseudodifferential Operators, 247–81. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511569425.010.
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