Related papers: Continuous symmetrization via polarization
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at…
Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The…
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…
We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…
In crystalline solids, the electronic polarization follows the \emph{generalized Neumann's principle}, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry…
We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also…
A fundamental result by L. Solomon in algebraic combinatorics and representation theory states that Mackey formulas for products of characters of a symmetric group, or equivalently the computation of tensor products of representations…
This paper shows that quantization of $\pi$-finite spaces, as a functor out of a higher category of spans, is equivariant in two ways: Symmetries of a given polarization/Lagrangian always induce coherent symmetries of the quantization. On…
We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini's…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions.…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first…
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second…
We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the…
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…