Related papers: Intertwining wave operators, Fourier restriction, …
We give the sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of…
Subject of the paper deals with the perturbation theory of linear operators acting in Hilbert space. For a certain class of perturbations the question is considered about existence of transformation operators implementing linear similarity…
We calculate the $(\mathfrak{g},K)$ module structure for the principal series representation of $Sp(4,\mathbb{R})$. Furthermore, we introduced a hypergeometric generating function together with an inverse Mellin transform technique as an…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as…
We prove, for a class of first order differential operators containing the generalized gradients, Dirac and Penrose twistor operators, a family of Kato inequalities that interpolates between the classical and the refined Kato. For the…
The main result is a construction, via the quantum dilogarithm, of certain intertwiner operators, which play the crucial role in the quantization of the cluster X-varieties and construction of the corresponding canonical representation.
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.
We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrodinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the…
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…
We give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering…
We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast Physics literature on related topics, we then study how much the…
We study a dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrodinger equation. Grebert and Thomann proved that there exist solutions with initial data…
We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved…
This manuscript focus on in the transmission problem for one dimensional waves with nonlinear weights on the frictional damping and time-varying delay. We prove global existence of solutions using Kato's variable norm technique and we show…
The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of…
Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep…
The confinement of plasmas in tokamaks and stellarators depends on magnetic field lines lying in nested toroidal surfaces. The transition near the plasma edge away from the lines lying in magnetic surfaces defines properties of divertors.…