Abstract. In this paper wavelet packet bases are used for an estimation of the autoregressive Hilbertian processes operator. We assume that integral operator kernel can have some singular structures and estimate them by projecting functional processes on suitable bases. Linear methods for continuous-time prediction using Hilbert-valued autoregressive processes are compared with the suggested me...

Abstract This article sketches a new analysis of the diachronic development found in many West Germanic languages from hybrid VO-OV order to rigid OV or VO order. The discussion departs discussions Struik & Van Kemenade ( 2020 / 2022 ) and Schoenmakers (to appear) on English/Dutch, which focus role object shift information structure. My interpretation their data will be based an earlier Bro...

We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. We next show that this result is best possible by including a result of N.J. Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two...

We prove that there is an orthonormal basis for square-integrable (waveform) cuspforms on SL2(Z)\H. First, we reconsider the well-known fact that the Hilbert space L(T) on the circle T = R/2πZ has an orthogonal Hilbert-space basis of exponentials e with n ∈ Z, using ideas relevant to situations lacking analogues of Dirichlet or Fejer kernels. These exponentials are eigenfunctions for the Laplac...

This paper examines the effective representation of the punctual Hilbert scheme. We give new equations, which are simpler than Bayer and Iarrobino-Kanev equations. These new Plücker-like equations define the Hilbert scheme as a subscheme of a single Grassmannian and are of degree two in the Plücker coordinates. This explicit complete set of defining equations for Hilb(P) are deduced from the co...

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (co...

In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...