Search results for "Spectral theory"
showing 10 items of 154 documents
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Hilbert space operators with two-isometric dilations
2021
A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or dilations to $2$-isometries. The adjoint of an operator which admits such liftings is characterized as the restriction of a backward shift on a Hilbert space of vector-valued analytic functions. These results are applied to concave operators (i.e., operators $S$ such that $S^{*2}S^{2} - 2 S^{*}S + I \le 0$) and to operators similar to contractions or isometries. Two types of liftings to $2$-isometries, as well as the extensions induced by them, are construct…
"Table 1" of "Measurement of the (anti-)$^{3}$He elliptic flow in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"
2020
Event-plane resolution $R_{\Psi_{2}}$ of the second harmonic as a function of the collision centrality.
Polaroid operators and Weyl type theorems
2015
Weyl type theorems have been proved for a considerably large number of classes of operators. In this work, after introducing the class of polaroid operators and some notions from local spectral theory, we determine a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. The theory is exemplified by given several examples of hereditarily polaroid operators.
Pseudodifferential Analysis on Manifolds with Boundary — a Comparison of b-Calculus and Cone Algebra
2001
We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose’s (overblown) b-calculus and Schulze’s cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
SOME SPECTRAL PROPERTIES OF MULTIPLIERS ON SEMI-PRIME BANACH ALGEBRAS
1995
Abstract We extend to arbitrary semi-prime Banach algebras some results of spectral theory and Fredholm theory obtained in [1] and [2] for multipliers defined in commutative semi-simple Banach algebras.
Fourier integral operators and inhomogeneous Gevrey classes
1988
Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.
Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials
2013
For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant.
Calderón problem for the p-Laplace equation : First order derivative of conductivity on the boundary
2016
We recover the gradient of a scalar conductivity defined on a smooth bounded open set in Rd from the Dirichlet to Neumann map arising from the p-Laplace equation. For any boundary point we recover the gradient using Dirichlet data supported on an arbitrarily small neighbourhood of the boundary point. We use a Rellich-type identity in the proof. Our results are new when p 6 = 2. In the p = 2 case boundary determination plays a role in several methods for recovering the conductivity in the interior. peerReviewed
PT Symmetry and Weyl Asymptotics
2012
For a class of PT-symmetric operators with small random perturbations, the eigenvalues obey Weyl asymptotics with probability close to 1. Consequently, when the principal symbol is nonreal, there are many nonreal eigenvalues.