相关论文: Poisson summation for Hankel transforms
We generalize the prescription realizing classical Poisson-Lie T-duality as canonical transformation to Poisson-Lie T-plurality. The key ingredient is the transformation of left-invariant fields under Poisson-Lie T-plurality. Explicit…
In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in $\RP^n$, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We…
We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized…
We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I. We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of…
We present a survey of results related to the solution of Kolmogorov--Nikolsky problem for Fourier sums on the classes of generalized Poisson integrals $C^{\alpha,r}_{\beta,p}$, which consists in finding of asymptotic equalities for exact…
The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson-Lie group is given. It is shown that the graded Poisson-Lie structures derived before for $GL(N)$ and $SL(N)$ are the special cases…
The article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of…
In this paper an extension of the concept of Geronimus transformation for sequences of $d$-orthogonal polynomials $\{P_n\}$ is introduced. The transformed sequences $\{P^{(k)}_n\}$, for $ k=1,\ldots, d,$ are analyzed and some relationships…
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…
We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…
The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions…
In this paper, we estimate the shifted convolution sum \[\sum_{n\geqslant1}\lambda_1(1,n)\lambda_2(n+h)V\Big(\frac{n}{X}\Big),\] where $V$ is a smooth function with support in $[1,2]$, $1\leqslant|h|\leqslant X$, $\lambda_1(1,n)$ and…
For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…
We generalize the result of Wirsing on Gauss transformation to the generalized tranformation $T_p(x)=\{\cfrac{p}{x}\}$ for any positive integer $p$. We give an estimate for the generalized Gauss-Kuzmin-Wirsing constant.
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
The purpose of this work is to provide a common combinatorial framework for some of the analogues and generalizations of Kazhdan-Lusztig R-polynomials that have appeared since the introduction of these remarkable polynomials (e.g.,…
This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It…
We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson-Lie group $GL_n$ and derive from it a generalized cluster structure on $GL_n$ compatible with the push-forward…
It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson…
The aim of this paper is to give the characterisation of the L p Range (p $\ge$ 2) of the Generalised Poisson Transform of the Hyperbolic space B(H n), (n $\ge$ 2), over the classical field of the quaternions H. Namely, if f is an…