Related papers: On integration with respect to filter
Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental…
In this article we discuss a generalized Wirtinger inequality.
The aim of this paper is to introduce and study graded and filtered gamma rings and gamma modules. We prove that the filtered $\Gamma$-ring (module) is a generalization of the notion of graded ring (module). Also, we construct a graded…
In this paper, we propose a generalization of a congruence due to Carlitz.
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
We approach the Riemann integral via generalized primitives to give a new proof for a general result on change of variable originally proven by Kestelman and Davies. Our proof is similar to Kestelman's, but we hope readers will find it…
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
In analogy with the classical theory of filters, for finitely complete categories, we provide the concepts of filter, G-neighborhood (short for \Grothendieck-neighborhood") and cover-neighborhood of a point, with the aim of studying…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.