A Hybrid Nonparametric Framework for Outlier Detection in Functional Time Series
ABSTRACT Outlier detection in functional time series is challenging due to temporal dependence and the simultaneous presence of magnitude, shape, and partial anomalies. Existing methods often assume independence or rely on model based approaches, such as the Standard Smoothed Bootstrap on Residuals (SmBoR), which may not work well if the model is ...
David Solano +4 more
wiley +1 more source
Optimal Control of the Viscous Wave Equation via the Pontryagin Maximum Principle
ABSTRACT A tracking‐type optimal control problem governed by the viscous wave equation with a distributed‐source control and L2$$ {L}^2 $$‐L1$$ {L}^1 $$ control costs is investigated. For this class of PDE‐constrained linear‐convex problems, a Pontryagin maximum principle (PMP) in the PDE setting is derived, and it is shown that the pointwise ...
A. Borzì, S. Roy
wiley +1 more source
Variable Lebesgue Space over Weighted Homogeneous Tree
An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space Lp(·)(μ) over (V,d,μ) and investigate it under the
Yuxun Zhang, Jiang Zhou
openaire +1 more source
Change Point Analysis for Functional Data Using Empirical Characteristic Functionals
ABSTRACT We develop a new method to detect change points in the distribution of functional data based on integrated CUSUM processes of empirical characteristic functionals. Asymptotic results are presented under conditions allowing for low‐order moments and serial dependence in the data establishing the limiting null‐distribution of the proposed test ...
Lajos Horváth +2 more
wiley +1 more source
Characterization of mean value harmonic functions on norm induced metric\n measure spaces with weighted Lebesgue measure [PDF]
Antoni Kijowski
openalex +1 more source
Fourier analytic properties of Kakeya sets in finite fields
Abstract We prove that a Kakeya set in a vector space over a finite field of size q$q$ always supports a probability measure, whose Fourier transform is bounded by q−1$q^{-1}$ for all non‐zero frequencies. We show that this bound is sharp in all dimensions at least 2.
Jonathan M. Fraser
wiley +1 more source
In this paper, we studied the issues of integrability with the weight of the sum of series with respect to multiplicative systems, provided that the coefficients of the series are monotonic.
М.Ж. Тургумбаев +2 more
doaj +1 more source
Maximally dissipative and self‐adjoint extensions of K$K$‐invariant operators
Abstract We introduce the notion of K$K$‐invariant operators, S$S$, in a Hilbert space, with respect to a bounded and boundedly invertible operator K$K$ defined via K∗SK=S$K^*SK=S$. Conditions such that self‐adjoint and maximally dissipative extensions of K$K$‐invariant symmetric operators are also K$K$‐invariant are investigated.
Christoph Fischbacher +2 more
wiley +1 more source
Maximal Regularity in Exponentially Weighted Lebesgue Spaces of the Stokes Operator in Unbounded Cylinders [PDF]
Myong‐Hwan Ri, Reinhard Farwig
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
wiley +1 more source

