The Experts below are selected from a list of 66255 Experts worldwide ranked by ideXlab platform
Karlmikael Perfekt - One of the best experts on this subject based on the ideXlab platform.
-
plasmonic eigenvalue problem for corners limiting absorption principle and absolute continuity in the Essential Spectrum
Journal de Mathématiques Pures et Appliquées, 2020Co-Authors: Karlmikael PerfektAbstract:Abstract We consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann–Poincare operator of the boundary. A limiting absorption principle is proved, valid when the spectral parameter approaches the Essential Spectrum. Putting the principle into use, it is proved that the corner produces absolutely continuous Spectrum of multiplicity 1. The embedded eigenvalues are discrete. In particular, there is no singular continuous Spectrum.
-
plasmonic eigenvalue problem for corners limiting absorption principle and absolute continuity in the Essential Spectrum
arXiv: Spectral Theory, 2019Co-Authors: Karlmikael PerfektAbstract:We consider the plasmonic eigenvalue problem for 2D domains with curvilinear corners, studying the spectral theory of the Neumann--Poincare operator of the boundary. A limiting absorption principle is proved, valid when the spectral parameter approaches the Essential Spectrum. Putting the principle into use, it is proved that the corner produces absolutely continuous Spectrum of multiplicity 1. The embedded eigenvalues are discrete. In particular, there is no singular continuous Spectrum.
-
the Essential Spectrum of the neumann poincare operator on a domain with corners
Archive for Rational Mechanics and Analysis, 2017Co-Authors: Karlmikael Perfekt, Mihai PutinarAbstract:Exploiting the homogeneous structure of a wedge in the complex plane, we compute the Spectrum of the anti-linear Ahlfors–Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors–Beurling transform and the Neumann–Poincare operator provides the Spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the Essential Spectrum of the Neumann–Poincare operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field.
Mihai Putinar - One of the best experts on this subject based on the ideXlab platform.
-
the Essential Spectrum of the neumann poincare operator on a domain with corners
Archive for Rational Mechanics and Analysis, 2017Co-Authors: Karlmikael Perfekt, Mihai PutinarAbstract:Exploiting the homogeneous structure of a wedge in the complex plane, we compute the Spectrum of the anti-linear Ahlfors–Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors–Beurling transform and the Neumann–Poincare operator provides the Spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the Essential Spectrum of the Neumann–Poincare operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field.
Vladimir Georgescu - One of the best experts on this subject based on the ideXlab platform.
-
on the Essential Spectrum of n body hamiltonians with asymptotically homogeneous interactions
Journal of Operator Theory, 2017Co-Authors: Vladimir Georgescu, Victor NistorAbstract:We determine the Essential Spectrum of N-body Hamiltonians with 2-body (or, more generally, k-body) potentials that have radial limits at infinity. The classical N-body Hamiltonians appearing in the well known HVZ-theorem are a particular case of this type of potentials corresponding to zero limits at infinity. Our result thus extends the HVZ-theorem that describes the Essential Spectrum of the usual N-body Hamiltonians. More precisely, if the configuration space of the system is a finite dimensional real vector space X, then let e(X) be the C *-algebra of functions on X generated by the algebras C(X/Y), where Y runs over the set of all linear subspaces of X and C(X/Y) is the space of continuous functions on X/Y that have radial limits at infinity. This is the algebra used to define the potentials in our case, while in the classical case the C(X/Y) are replaced by C0 (X/Y). The proof of our main results is based on the study of the structure of the algebra e(X), in particular, we determine its character space and the structure of its cross-product e(X) := e(X) ⋊ X by the natural action τ of X on e(X). Our techniques apply also to more general classes of Hamiltonians that have a many-body type structure. We allow, in particular, potentials with local singularities and more general behaviours at infinity. We also develop general techniques that may be useful for other operators and other types of questions, such as the approximation of eigenvalues.
-
on the Essential Spectrum of n body hamiltonians with asymptotically homogeneous interactions
arXiv: Spectral Theory, 2015Co-Authors: Vladimir Georgescu, Victor NistorAbstract:We determine the Essential Spectrum of Hamiltonians with N-body type interactions that have radial limits at infinity. This extends the HVZ-theorem, which treats perturbations of the Laplacian by potentials that tend to zero at infinity. Our proof involves $C^*$-algebra techniques that allows one to treat large classes of operators with local singularities and general behavior at infinity. In our case, the configuration space of the system is a finite dimensional, real vector space $X$, and we consider the $C^*$-algebra $\mathcal{E}(X)$ of functions on $X$ generated by functions of the form $v\circ\pi_Y$, where $Y$ runs over the set of all linear subspaces of $X$, $\pi_Y$ is the projection of $X$ onto the quotient $X/Y$, and $v:X/Y\to\mathbb{C}$ is a continuous function that has uniform radial limits at infinity. The group $X$ acts by translations on $\mathcal{E}(X)$, and hence the crossed product $\mathscr{E}(X) := \mathcal{E}(X)\rtimes X$ is well defined; the Hamiltonians that are of interest to us are the self-adjoint operators affiliated to it. We determine the characters of $\mathcal{E}(X)$. This then allows us to describe the quotient of $\mathscr{E}(X)$ with respect to the ideal of compact operators, which in turn gives a formula for the Essential Spectrum of any self-adjoint operator affiliated to $\mathscr(X)$.
-
the Essential Spectrum of n body systems with asymptotically homogeneous order zero interactions
Comptes Rendus Mathematique, 2014Co-Authors: Vladimir Georgescu, Victor NistorAbstract:Abstract We study the Essential Spectrum of N -body Hamiltonians with potentials defined by functions that have radial limits at infinity. The results extend the HVZ theorem which describes the Essential Spectrum of usual N -body Hamiltonians. The proof is based on a careful study of algebras generated by potentials and their cross-products. We also describe the topology on the Spectrum of these algebras, thus extending to our setting a result of A. Mageira. Our techniques apply to more general classes of potentials associated with translation invariant algebras of bounded uniformly continuous functions on a finite-dimensional vector space X .
-
on the structure of the Essential Spectrum of elliptic operators on metric spaces
Journal of Functional Analysis, 2011Co-Authors: Vladimir GeorgescuAbstract:Abstract We give a description of the Essential Spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main result concerns the ideal structure of the C ⁎ -algebra generated by them.
-
localizations at infinity and Essential Spectrum of quantum hamiltonians i general theory
Reviews in Mathematical Physics, 2006Co-Authors: Vladimir Georgescu, Andrei IftimoviciAbstract:We isolate a large class of self-adjoint operators H whose Essential Spectrum is determined by their behavior at x ~ ∞ and we give a canonical representation of σess(H) in terms of spectra of limits at infinity of translations of H.
S A Nazarov - One of the best experts on this subject based on the ideXlab platform.
-
effects of rayleigh waves on the Essential Spectrum in perturbed doubly periodic elliptic problems
Integral Equations and Operator Theory, 2017Co-Authors: F L Bakharev, S A Nazarov, Giuseppe Cardone, Jari TaskinenAbstract:We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the Essential Spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.
-
a gap in the Essential Spectrum of a cylindrical waveguide with a periodic aperturbation of the surface
Mathematische Nachrichten, 2010Co-Authors: Giuseppe Cardone, S A Nazarov, Carmen PerugiaAbstract:It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the Essential Spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the cylinder are small, the gap certainly opens. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
-
Essential Spectrum of a periodic elastic waveguide may contain arbitrarily many gaps
Applicable Analysis, 2010Co-Authors: S A Nazarov, Keijo Ruotsalainen, Jari TaskinenAbstract:We construct a family of periodic elastic waveguides Π h , depending on a small geometrical parameter, with the following property: as h → +0, the number of gaps in the Essential Spectrum of the elasticity system on Π h grows unboundedly.
-
a criterion for the existence of the Essential Spectrum for beak shaped elastic bodies
Journal de Mathématiques Pures et Appliquées, 2009Co-Authors: Giuseppe Cardone, S A Nazarov, Jari TaskinenAbstract:Abstract We establish a criterion for the existence of the Essential Spectrum for the elasticity problem in the case the traction-free surface of a finite elastic body has a beak-shaped irregularity (see Corollary 3.5 and Theorem 4.2). This boundary irregularity is angular in two dimensions and cuspidal in one dimension. We obtain further information on the spectral structure in some particular cases, and formulate open questions and hypotheses.
-
gaps in the Essential Spectrum of periodic elastic waveguides
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2009Co-Authors: C Cardone, Vincenzo Minutolo, S A NazarovAbstract:Examples of periodic elastic waveguides are constructed, the Essential Spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete Spectrum only. The gap is detected with the help of an inequality of Korn's type and the max-min principle for eigenvalues of self-adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the Essential Spectrum can include eigenvalues in the point Spectrum.
Luis O. Silva - One of the best experts on this subject based on the ideXlab platform.
-
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.
-
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 paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator’s Essential Spectrum. The case of the spectral parameter being an eigenvalue is also considered. It is also shown that if the matrix entries commute, then the estimates can be refined. Finally, various examples of block Jacobi operators are given to illustrate the results.
