The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...
This dissertation develops geometric variational models for different inverse problems in imaging that are ill-posed, designing at the same time efficient numerical algorithms to compute their solutions. Variational methods solve inverse problems by the fo ...
The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...
We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...
This paper describes an iterative solution technique for partial differential equations involving the grad(div) operator, based on a domain decomposition. Iterations are performed to solve the solution on the interface. We identify the transmission relatio ...
When producing a mosaic of multiple multi-spectral images one needs to harmonize the colours so that the tone transition is smooth from one image to the other. Given two images Im(a) and Im(b), a transform T is sought to map Im(b) to an image that is harmo ...
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We build wavelet-like functions based on a parametrized family of pseudo-differential operators Lv that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...
Iterative models are widely used today in CAD. They allow, with a limited number of parameters, to represent relatively complex forms through a subdivision algorithm. There is a wide variety of such models (Catmull-Clark, Doo-Sabin, L-Systems...). Most ite ...
The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...
