Related papers: On Wigner transforms in infinite dimensions
We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…
Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…
We completely characterize the range of $L^p$-boundedness of certain multilinear Radon-like transforms involving vertical projections in the Heisenberg group.
We use the tridiagonal representation approach to obtain an exact solution of the three-dimensional radial Schr\"odinger equation for a spiked oscillator with inverse quartic singularity and for all angular momenta. The solution is a finite…
We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the…
We review recent probabilistic results on covariant Schr\"odinger operators on vector bundles over (possibly locally infinite) weighted graphs, and explain applications like semiclassical limits. We also clarify the relationship between…
It is shown that vielbeins and connections of any (super)space are naturally described in terms of nonlinear realizations of infinite - dimensional diffeomorphism groups of the corresponding (super)space. The method of construction of…
We give a complete analysis of the projective unitary irreducible representations of the Poincar\'e group in 1+2 dimensions applying Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrodinger groupes for a very large class of real-valued potentials.
We review the papers on the Jordan-Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two-dimensional spin-1/2 models. We discuss in some detail the two-dimensional…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…
In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example…
We study integral estimates of maximal functions for Schr\"odinger means.
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to $t$-dependent Schr\"odinger equations on separable (possibly infinite-dimensional) Hilbert…
Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrodinger equations in dimensions $n\neq 1$. Both focusing and defocusing cases of a power nonlinearity are considered,…
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.