Cyrille SICLET and Pierre SIOHAN France Télécom R&D (DMR); 4, rue du Clos Courtel; BP59; 35512 Cesson Sévigné; France Tel: +(33)299 12 38 35; Fax: +(33)299 12 40 98; E-mail: [email protected] Abstract— A new system of multicarrier modulation is described which takes advantage of the biorthogonality property to generalize the OFDM/OQAM technique into a Biorthogonal Frequency Div...

Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in Hilbert spaces of analytic functions (Nakazi, 1984) to linear regression in statistics (Box and Tiao, 1975). We unify these results via a finitedimensional duali...

Given a representation of a unimodular locally compact group, we discuss criteria for associated coherent state expansions in terms of the commuting algebra. It turns out that for those representations that admit such expansions there exists a unique finite trace on the commuting algebra such that the admissible vectors are precisely the tracial vectors for that trace. This observation is immed...

Lanczos vectors computed in nite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality. One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vectors at each step. For the symmetric case, there is a compromise approach. This compromise, known as maintaining semi-orthogonality, minimizes the cost of re-orthogonalization. This p...

We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree p in one dimension. In contrast to earlier approaches, these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree p − 1. Working with Gauß–Lobatto nodes, we find an interesting ...

This work presents an adaptive block Lanczos method for large-scale non-Hermitian Eigenvalue problems (henceforth the ABLE method). The ABLE method is a block version of the non-Hermitian Lanczos algorithm. There are three innovations. First, an adaptive blocksize scheme cures (near) breakdown and adapts the blocksize to the order of multiple or clustered eigenvalues. Second, stopping criteria ...

Derivation of the self-consistent multimode laser equations. The Green function which forms the kernel of the fundamental self-consistent equation Eq. 1 has a non-hermitian spectral representation of the form (S1) G(x, x ′ ; k) = ∞ m=1 ϕ m (x, k) ¯ ϕ * m (x ′ , k) 2 k a (k − k m (k)). (S1) where the CF states ϕ m (x, k) satisfy the equation − 1 ǫ(x) ∇ 2 ϕ m (x, k) = k 2 m (k) ϕ m (x, k) (S2) wi...

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

We introduce the sequence of generalized Gon£arov polynomials, which is a basis for the solutions to the Gon£arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon£arov basis is a sequence (tn(x))n≥0 of polynomials de ned by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, a...

Originating from automated theorem proving, deduction modulo removes computational arguments from proofs by interleaving rewriting with the deduction process. From a proof-theoretic point of view, deduction modulo defines a generic notion of cut that applies to any first-order theory presented as a rewrite system. In such a setting, one can prove cut-elimination theorems that apply to many theo...