Related papers: Gordon type Theorem for measure perturbation
In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…
A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to…
On this short note, we apply the Mourre theory of the limiting absorption with {\it difference} type conditions on the potential, instead of conditions on the derivatives. In order that we modify the definition of the conjugate operator,…
The goal of this paper is to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category O for the rational Cherednik algebra of type G(r,p,n). As a first application, we give a…
We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularly implies the existence and H\"{o}lder continuity of the…
Two comparison theorems are established for discrete eigenvalues of the Klein-Gordon equation with an attractive central vector potential in d >= 1 dimensions. (I) If \psi_1 and \psi_2 are node-free ground states corresponding to positive…
In this paper, Morgan type uncertainty principle and unique continuation properties of abstract Schr\"odinger equations with time dependent potentials in vector-valued classes are obtained. The equation involves a possible linear operators…
The problem of covariance of physical quantities has not been solved fundamentally in the theory of relativity, which has caused a lot of confusion in the community; a typical example is the Gordon metric tensor, which was developed almost…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
We study equations driven by Schr\"odinger operators consisting of a self-adjoint Dirichlet operator and a singular potential, which belongs to a class of positive Borel measures absolutely continuous with respect to a capacity generated by…
We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate…
We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative…
We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all scales is sufficient. Our proof uses a technique we call the…
Using the notion of higher-order Fourier dimension introduced in \cite{M2} (which was a sort of psuedorandomness condition stemming from the Gowers norms of Additive Combinatorics), we prove a maximal theorem and corresponding…
We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of…
We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.
We prove dispersive estimates for Schroedinger operators in dimension three without any assumptions on zero energy. Ie, we allows resonances and/or eigenvalues at zero energy.
As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators and use these ideas to give a characterization of diagonals…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
We study the perturbation theory for three dimensional Chern--Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the…