Related papers: On integration with respect to filter

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of…

Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…

In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…

The goals of this paper are first to describe and then to apply an ergodic-theoretic generalization of the Siegel integral formula from the geometry of numbers. The general formula will be seen to serve both as a guide and as a tool for…

Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…

We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model…

This paper is a continuation of our recent paper with the same title, arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that…

In this note, we propose an integral representation for $\zeta(4)$, where $\zeta$ is the Riemann zeta function. The corresponding expression is obtained using relations for polylogarithms. A possible generalization to any even argument of…

In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real…

Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to model the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters, clarifying what guarantees…

We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.

We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.

In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.

We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of…

We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.

We study Riemann-Lebesgue integrability of a vector function relative to an arbitrary non-negative set function. We obtain some classical integral properties. Results regarding the continuity properties of the integral and relationships…