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Convergence Almost Everywhere and Divergence Everywhere of Taylor and Dirichlet Series
Real Analysis Exchange, 2004 Nine theorems are proved. The following ones are typical. Theorem 3.2. There exists a Dirichlet series \[ f(x):= \sum^\infty_{n=1} a_n n^{-s} \] with convergence and boundedness in the half-plane \(\mathbb{C}_0:=\{s\in\mathbb{C}:\text{Re}(s)> 0\}\), and such that \(\sum a_n n^{it}\) diverges for each \(t\in\mathbb{R}\). Theorem 5.3. Let \((a_n\geq 1)\)
Bayart, F. +2 more
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Almost everywhere convergence of series in 𝐿¹ [PDF]
Proceedings of the American Mathematical Society, 2005 We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence ( c i
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Social distancing is a social dilemma game played by every individual against his/her population
PLoS ONE, 2021 Since the outbreak of the global COVID-19 pandemic, social distancing has been known to everyone and recommended almost everywhere everyday. Social distancing has been and will be one of the most effective measures and sometimes, the only available one ...
Zhijun Wu
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Abstract and Applied Analysis, 2013 We study almost everywhere convergence for Riesz means related to Schrödinger operator with constant magnetic fields. Through researching the weighted norm estimates for the maximal operator with power-weight functions, we obtain the desired result ...
Liurui Deng, Bolin Ma
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NSVQ: Noise Substitution in Vector Quantization for Machine Learning
IEEE Access, 2022 Machine learning algorithms have been shown to be highly effective in solving optimization problems in a wide range of applications. Such algorithms typically use gradient descent with backpropagation and the chain rule.
Mohammad Hassan Vali, Tom Backstrom
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Rearrangement and Convergence in Spaces of Measurable Functions
Journal of Inequalities and Applications, 2007 We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence ...
A. Trombetta +2 more
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Matrix Summability of Walsh–Fourier Series
Mathematics, 2022 The presented paper discusses the matrix summability of the Walsh–Fourier series. In particular, we discuss the convergence of matrix transforms in L1 space and in CW space in terms of modulus of continuity and matrix transform variation.
Ushangi Goginava, Károly Nagy
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New characterizations of magnetic Sobolev spaces
Advances in Nonlinear Analysis, 2018 We establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis and Mironescu. The second one is related to the work of
Nguyen Hoai-Minh +3 more
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Space-Time Estimates on Damped Fractional Wave Equation
Abstract and Applied Analysis, 2014 We obtain space-time estimates on the solution u(t,x) to the Cauchy problem of damped fractional wave equation. We mainly focus on the linear equation.
Jiecheng Chen, Dashan Fan, Chunjie Zhang
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Invariant intuitionistic fuzzy observables [PDF]
Notes on IFSThe aim of this contribution is showed that a sequence of Cesaro means of intuitionistic fuzzy observables has an invariant limit m-almost everywhere, where m is an intuitionistic fuzzy state.
Katarína Cunderlıková
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