相关论文: Poisson summation for Hankel transforms
\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}
We provide a context around a conjectured closed form for the Hankel transform of linear combinations of consecutive pairs of Catalan numbers. This generalizes the formula for the Hankel transforms of the shifted Catalan numbers and the…
We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the…
Our concern is with Riemannian symmetric spaces $Z=G/K$ of the non-compact type and more precisely with the Poisson transform $\mathcal{P}_\lambda$ which maps generalized functions on the boundary $\partial Z$ to $\lambda$-eigenfunctions on…
We give an $L_\infty$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again the explicit formulas for all the formal…
We consider generalizations of pairing relations for Kovalevskaya exponents in quasihomogeneous systems with quasihomogeneous tensor invariants. The case of presence of a Poisson structure in the system is investigated in more detail. We…
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
We prove the Freiheitssatz for the variety of generic Poisson algebras.
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used…
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…
We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.
In the present paper the authors show that iterations of the Hankel transform with $\mathscr{K}_{\nu}$-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval-Goldstein type theorems for…
For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a general procedure for constructing Baecklund transformation is proposed. The…
In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel transform of the first form (q,…
The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in…
The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic…
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 with order $1/2$ in convex domains but has a reduced…
Poisson's equation is fundamental to the study of Markov chains, and arises in connection with martingale representations and central limit theorems for additive functionals, perturbation theory for stationary distributions, and average…
The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This defines a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister…
The notions of Poisson $H$-pseudoalgebras are generalizations of Poisson algebras in a pseudotensor category $\mathcal{M}^{\ast}(H)$. This paper introduces an analogue of Poisson-Ore extension in Poisson $H$-pseudoalgebras. Poisson…