Results 61 to 70 of about 148 (138)

On a Relation to Hilbert's Integral Inequality and a Hilbert-Type Inequality

Kyungpook mathematical journal, 2009
In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.
openaire   +2 more sources

Adaptive Estimation for Weakly Dependent Functional Times Series

Journal of Time Series Analysis, EarlyView.
ABSTRACT We propose adaptive mean and autocovariance function estimators for stationary functional time series under 𝕃p−m‐approximability assumptions. These estimators are designed to adapt to the regularity of the curves and to accommodate both sparse and dense data designs.
Hassan Maissoro, Valentin Patilea, Myriam Vimond   +2 more
wiley   +1 more source

Equivalent properties of a reverse half-discrete Hilbert’s inequality

Journal of Inequalities and Applications, 2019
By using the weight functions, the idea of introduced parameters and the Euler–Maclaurin summation formula, a reverse half-discrete Hilbert’s inequality with the homogeneous kernel and the reverse equivalent forms are given (for ...
Ai-zhen Wang, Bi-cheng Yang, Qiang Chen
doaj   +1 more source

Density‐Valued ARMA Models by Spline Mixtures

Journal of Time Series Analysis, EarlyView.
ABSTRACT This paper proposes a novel framework for modeling time series of probability density functions by extending autoregressive moving average (ARMA) models to density‐valued data. The method is based on a transformation approach, wherein each density function on a compact domain [0,1]d$$ {\left[0,1\right]}^d $$ is approximated by a B‐spline ...
Yasumasa Matsuda, Rei Iwafuchi
wiley   +1 more source

On a New Hilbert-Type Intergral Inequality with the Intergral in Whole Plane

Journal of Inequalities and Applications, 2010
By introducing some parameters and estimating the weight functions, we build a new Hilbert's inequality with the homogeneous kernel of 0 order and the integral in whole plane. The equivalent inequality and the reverse forms are considered.
Xie Zitian, Zeng Zheng
doaj  

A Note on Local Polynomial Regression for Time Series in Banach Spaces

Journal of Time Series Analysis, EarlyView.
ABSTRACT This work extends local polynomial regression to Banach space‐valued time series for estimating smoothly varying means and their derivatives in non‐stationary data. The asymptotic properties of both the standard and bias‐reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates.
Florian Heinrichs
wiley   +1 more source

On the Hubert Inequality

Zeitschrift für Analysis und ihre Anwendungen, 1999
It is shown that the Hilbert inequality for double series can be improved by introducing the positive real number \frac{1}{\pi^2} (\frac{s^2(b)}{\|a\|^2} + \frac{s^2(b)}{\|b\|^2}) where s(x) = \sum^{\infty ...
openaire   +3 more sources

On the extended Hardy–Hilbert's inequality

Journal of Mathematical Analysis and Applications, 2002
In this paper, the authors prove a number of interesting inequalities of the Hardy-Hilbert type. Their results improve and generalize both the discrete and continuous Hardy-Hilbert inequalities obtained by \textit{B. Yang} and \textit{L. Debnath} [J. Math. Anal. Appl. 233, No.~2, 484-497 (1999; Zbl 0935.26009)] and \textit{B. Yang} [J. Math. Anal. Appl.
Yang, Bicheng, Debnath, Lokenath
openaire   +2 more sources

On the Existence of One‐Sided Representations for the Generalised Dynamic Factor Model

Journal of Time Series Analysis, EarlyView.
ABSTRACT We study the Generalised Dynamic Factor Model (GDFM) and show that the dynamic common component, that is, the common component of the GDFM, can be expressed using only current and past observations under mild assumptions. Specifically, we require (i) the dynamic common component to be purely non‐deterministic and (ii) the exclusion of ...
Philipp Gersing
wiley   +1 more source

On Hardy–Hilbert's Integral Inequality

Journal of Mathematical Analysis and Applications, 2001
By the Hardy-Hilbert's integral inequality, the author refers to the inequality \[ \int^\infty_0\int^\infty_0 \frac{f(x)g(y)}{x+y} dx dy < \frac{\pi}{\sin\Big(\frac{\pi}{p}\Big)}\Big(\int^\infty_0 f^{p}(t) dt\Big)^{1/p} \Big(\int^\infty_0 g^{q}(t) dt\Big)^{1/q} \] [cf. \textit{G. H. Hardy, J. E. Littlewood} and \textit{G.
openaire   +1 more source