Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Hei...

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sen...

Let (xn) ⊂ R d be a uniformly separated sequence which forms a Fourier frame for PWB2 , the space of square-integrable functions on R d whose Fourier transforms vanish outside the Euclidean unit ball B2. Given λ > 0 and f ∈ PWB2 , there is a unique sequence (aj) in l2 such that the function Iλ(f)(x) := X aje −λ‖x−xj‖ 2 2 , x∈R d , is continuous and square integrable on R, and satisfies the inte...

In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer-Schweizer d...

The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of twoand three-state vertex models. These models include the six-vertex model, the 15-vertex A (1) 2 model and the 19-vertex models of Izergin-Korepin and ZamolodchikovFateev. In each case the eigenspectra is determined by a...

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold M to finite-dimensional Lie group, by means complete orthonormal bases for Hermitian inner product on the and Fourier expansion. The Peter–Weyl theorem case manifolds related groups coset spaces discussed, appropriate Hilbert space L2(M) square-integrable functions are constructed. It shown that ...

Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schrödinger operator with square integrable potential.

We compute the Wiener-Poisson expansion of square-integrable functionals of a nite number of Poisson jump times in series of multiple Poisson stochastic integrals.

Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schrödinger operator with square integrable potential.