Hunt convolution kernels which are continuous singular with respect to Haar measure

1979 ◽  
pp. 10-21 ◽  
Author(s):  
Christian Berg
Keyword(s):  
Haar Measure ◽  
Convolution Kernels

scholarly journals Characterization of Relative Domination Principle

1973 ◽  
Vol 50 ◽  
pp. 175-184 ◽  
Author(s):  
Isao Higuchi ◽  
Masayuki Itô
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Radon Measure ◽  
Convolution Type ◽  
Convolution Kernel ◽  
Locally Compact ◽  
Positive Radon Measure ◽  
Convolution Kernels

Let X be a locally compact and σ-compact Abelian group and ξ be the Haar measure of X. A positive Radon measure N on X is called a convolution kernel when we regard it as a kernel of potentials of convolution type. M. Itô [4], [6] characterized the convolution kernel which satisfies the domination principle. The purpose of this paper is to characterize the relative domination principle for the convolution kernels.

scholarly journals The semi-balayability of real convolution kernels

1985 ◽  
Vol 99 ◽  
pp. 89-110 ◽  
Author(s):  
Masayuki Itô ◽  
Noriaki Suzuki
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Locally Compact ◽  
Convolution Kernels

Let X be a locally compact, σ-compact and non-compact abelian group. Throughout this paper, we shall denote by ξ a fixed Haar measure on X and by δ the Alexandroff point of X.

Beta dynamical systems over the formal fields

2014 ◽  
Vol 51 (4) ◽  
pp. 454-465
Author(s):  
Lu-Ming Shen ◽  
Huiping Jing
Keyword(s):  
Dynamical Systems ◽  
Finite Field ◽  
Haar Measure ◽  
Laurent Series ◽  
Formal Laurent Series ◽  
Almost All

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q ((X^{ - 1} ))$$ \end{document} denote the formal field of all formal Laurent series x = Σ n=ν∞anX−n in an indeterminate X, with coefficients an lying in a given finite field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}. For any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} with deg β > 1, it is known that for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} (with respect to the Haar measure), x is β-normal. In this paper, we show the inverse direction, i.e., for any x, for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document}, x is β-normal.

scholarly journals Compact groups with a set of positive Haar measure satisfying a nilpotent law

2021 ◽  
pp. 1-4
Author(s):  
ALIREZA ABDOLLAHI ◽  
MEISAM SOLEIMANI MALEKAN
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Positive Answer ◽  
Nilpotent Subgroup ◽  
Compact Groups

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

Application of convolution neural network in medical image processing

2020 ◽  
pp. 1-11
Author(s):  
Jie Liu ◽  
Hongbo Zhao
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Network Structure ◽  
Medical Image ◽  
Sampling Methods ◽  
Medical Image Processing ◽  
Convolution Neural Network ◽  
Data Set ◽  
Convolution Kernels ◽  
Neural Network Structure

BACKGROUND: Convolution neural network is often superior to other similar algorithms in image classification. Convolution layer and sub-sampling layer have the function of extracting sample features, and the feature of sharing weights greatly reduces the training parameters of the network. OBJECTIVE: This paper describes the improved convolution neural network structure, including convolution layer, sub-sampling layer and full connection layer. This paper also introduces five kinds of diseases and normal eye images reflected by the blood filament of the eyeball “yan.mat” data set, convenient to use MATLAB software for calculation. METHODSL: In this paper, we improve the structure of the classical LeNet-5 convolutional neural network, and design a network structure with different convolution kernels, different sub-sampling methods and different classifiers, and use this structure to solve the problem of ocular bloodstream disease recognition. RESULTS: The experimental results show that the improved convolutional neural network structure is ideal for the recognition of eye blood silk data set, which shows that the convolution neural network has the characteristics of strong classification and strong robustness. The improved structure can classify the diseases reflected by eyeball bloodstain well.

scholarly journals When the Whole Is Not Greater Than the Combination of Its Parts: A “Decompositional” Look at Compositional Distributional Semantics

2015 ◽  
Vol 41 (1) ◽  
pp. 165-173 ◽  
Author(s):  
Fabio Massimo Zanzotto ◽  
Lorenzo Ferrone ◽  
Marco Baroni
Keyword(s):  
Distributional Semantics ◽  
Important Class ◽  
Strong Link ◽  
Composition Methods ◽  
Convolution Kernels ◽  
Composition Operations ◽  
Compositional Distributional Semantics

Distributional semantics has been extended to phrases and sentences by means of composition operations. We look at how these operations affect similarity measurements, showing that similarity equations of an important class of composition methods can be decomposed into operations performed on the subparts of the input phrases. This establishes a strong link between these models and convolution kernels.

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