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Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

Applications · Statistics 2017-05-05 Huang Huang , Ying Sun

Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…

Methodology · Statistics 2025-02-04 Jongwook Kim , Chunfeng Huang , Nicholas Bussberg

The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional…

Classical Analysis and ODEs · Mathematics 2009-07-16 Ovidiu Costin , Stavros Garoufalidis

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…

Statistics Theory · Mathematics 2013-05-10 Victor M. Panaretos , Shahin Tavakoli

In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…

Functional Analysis · Mathematics 2024-07-08 Zunwei Fu , Xianming Hou , Qingyan Wu

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

Statistics Theory · Mathematics 2009-01-28 Jan Johannes

Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…

Statistics Theory · Mathematics 2017-11-28 Alfredo Alegría , Emilio Porcu , Reinhard Furrer

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

Probability · Mathematics 2024-11-18 Marc Jornet

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Complex Variables · Mathematics 2025-07-29 Samuel L. Krushkal

Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…

General Relativity and Quantum Cosmology · Physics 2024-12-17 Jorge Valencia , Rodrigo Tenorio , Maria Rosselló-Sastre , Sascha Husa

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity…

Numerical Analysis · Mathematics 2020-06-30 Lijing Zhao , Weihua Deng , Jan S Hesthaven

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms…

High Energy Physics - Phenomenology · Physics 2023-08-02 Kyle Lee , Ian Moult , Felix Ringer , Wouter J. Waalewijn

We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…

Statistics Theory · Mathematics 2024-07-03 Hendrik Paul Lopuhaä

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and…

Statistics Theory · Mathematics 2015-10-15 Fei Jiang , Yanyuan Ma , Yuanjia Wang

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schr\"odinger equation from which the expansion coefficents can be found.…

High Energy Physics - Theory · Physics 2009-10-30 Paul Mansfield , Marcos Sampaio , Jiannis Pachos

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…

General Relativity and Quantum Cosmology · Physics 2020-04-22 Maximilian Becker , Carlo Pagani , Omar Zanusso

The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…

Mathematical Physics · Physics 2019-05-13 William D. Kirwin , José Mourão , João P. Nunes , Thomas Thiemann

This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…

Functional Analysis · Mathematics 2015-06-17 Toni Heikkinen , Juha Kinnunen , Janne Korvenpää , Heli Tuominen

With the rapid development of wearable device technologies, accelerometers can record minute-by-minute physical activity for consecutive days, which provides important insight into a dynamic association between the intensity of physical…

Methodology · Statistics 2024-09-06 Cheng Cao , Jiguo Cao , Hao Pan , Yunting Zhang , Fan Jiang , Xinyue Li

In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and…

Classical Analysis and ODEs · Mathematics 2017-03-22 Christian Lavault