Related papers: Criterion for convergence almost everywhere, with …
We note that the Fubini theorem may be used to prove that an $L^1$ function is determined by its Fourier coefficients.
In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater…
We establish a connection between the $L^2$ norm of sums of dilated functions whose $j$th Fourier coefficients are $\mathcal{O}(j^{-\alpha})$ for some $\alpha \in (1/2,1)$, and the spectral norms of certain greatest common divisor (GCD)…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
In the classical literature on infinite series there are various tests to determine if a given infinite series converges, diverges, or oscillates. But unfortunately, for very many infinite series all the existing tests can fail to provide…
Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds \tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in…
The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions $f\in$ Lip1 class provides absolute convergence of Fourier series. In particular we found…
Several predictive algorithms are described. Highlighted are variants that make predictions by superposing fields associated to the training data instances. They operate seamlessly with categorical, continuous, and mixed data. Predictive…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their…
A q-type Holder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S_q[f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding others…
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.
In this paper, we investigate very general approximation kernels with special properties, called an approximate identity, and prove almost everywhere and norm convergence of these general methods, which consists of a class of summability…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
In every sphere of science, theories make predictions and experiments validate them. However, common experience suggests that theoretically predicted exact magnitude for a parameter, constitute a small subset of all the experimentally…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
Let $S_\lambda F(x)$ be the spherical partial sums of the multiple Fourier series of function $F\in L_2(\mathbb{T}^N)$. We prove almost-everywhere convergence $S_\lambda F(x)\rightarrow F(x)$ for functions in Sobolev spaces…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.