An equivalence theorem for a K-functional constructed by Beltrami–Laplace operator on symmetric spaces

Ouadih, S. El

doi:10.1007/s11868-020-00326-2

Cited by 9 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A substantial part of the classical harmonic analysis on Euclidean spaces is dealing with such notions as Sobolev and Besov spaces, Paley-Wiener (bandlimited) functions, K-functional, moduli of continuity, Hardy-Steklov smoothing operators. These topics and their numerous extensions and generalizations still attracting attention of many mathematicians: [4], [6], [7], [8], [9], [12], [16], [28], [30]- [32]. For the classical results see [1], [2], [5], [10], [15], [17], [33].…”

Section: Introductionmentioning

confidence: 99%

Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

Pesenson¹

2019

Contemporary Mathematics

View full text Add to dashboard Cite

We introduce and describe relations between Sobolev, Besov and Paley-Wiener spaces associated with three representations of the Lie group G of affine transformations of the line, also known as the "ax + b" group. These representations are: left and right regular representations and a representation in a space of functions defined on the half-line. The Besov spaces are described as interpolation spaces between respective Sobolev spaces in terms of the K-functional and in terms of a relevant moduli of continuity. By using a Laplace operators associated with these representations a scales of relevant Paley-Wiener spaces are developed and a corresponding L 2 -approximation theory is constructed in which our Besov spaces appear as approximation spaces. Another description of our Besov spaces is given in terms of a frequencylocalized Hilbert frames. A Jackson-type inequalities are also proven.

show abstract

Section: Introductionmentioning

confidence: 99%

Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

Pesenson¹

2019

Contemporary Mathematics

View full text Add to dashboard Cite

show abstract

“…Although point and line detection is very important in gray level discontinuity detection, edge detection is by far the most common method. Image edge detection is realized by using the extreme value of the first derivative (gradient operator) or the zero-crossing information of the second derivative (Laplace operator) [7]. Edge detection is the process of determining and locating sharp discontinuities in images.…”

Section: Introductionmentioning

confidence: 99%

A novel Gauss-Laplace operator based on multi-scale convolution for dance motion image enhancement

Shen¹,

Jiang²,

Teng³

2018

ICST Transactions on Scalable Information Systems

View full text Add to dashboard Cite

Traditional image enhancement methods have the problems of low contrast and fuzzy details. Therefore, we propose a novel Gauss-Laplace operator based on multi-scale convolution for dance motion image enhancement. Firstly, multi-scale convolution is used to preprocess the image. Then, we improve the traditional Laplace edge detection operator and combine it with Gauss filter. The Gaussian filter is used to smooth the image and suppress the noise, and the edge detection is processed based on the Laplace gradient edge detector. The detail image extracted by Gauss-Laplace operator and the image with brightness enhancement are linearly weighted fused to reconstruct the image with clear detail edge and strong contrast. Experiments are carried out with detailed images in different scenes. It is compared with traditional methods to verify the effectiveness of the proposed method.

show abstract

“…for rank one symmetric spaces [18], for Jacobi analysis in [17] and for compact symmetric spaces on [38]. In this paper our aim is to extend this characterization to more general setting of solvable (non unimodular) Lie groups.…”

mentioning

confidence: 99%

A note on $K$-functional, Modulus of smoothness, Jackson theorem and Nikolskii-Stechkin inequality on Damek-Ricci spaces

Kumar,

Ruzhansky

2020

Preprint

View full text Add to dashboard Cite

In this paper we study approximation theorems for L 2 -space on Damek-Ricci spaces. We prove direct Jackson theorem of approximations for the modulus of smoothness defined using spherical mean operator on Damek-Ricci spaces. We also prove Nikolskii-Stechkin inequality. To prove these inequalities we use functions of bounded spectrum as a tool of approximation. Finally, as an application we prove equivalence of the K-functional and modulus of smoothness for Damek-Ricci spaces. Contents 1. Introduction 2. Essentials about harmonic NA groups 3. Main results 3.1. Direct Jackson theorem 3.2. Nikolskii-Stechkin inequality

show abstract

An equivalence theorem for a K-functional constructed by Beltrami–Laplace operator on symmetric spaces

Cited by 9 publications

References 16 publications

Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

A novel Gauss-Laplace operator based on multi-scale convolution for dance motion image enhancement

A note on $K$-functional, Modulus of smoothness, Jackson theorem and Nikolskii-Stechkin inequality on Damek-Ricci spaces

Contact Info

Product

Resources

About