scholarly journals A Characterization of Multi-Wavelet Dual Frames in Sobolev Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Jianping Zhang ◽  
Jiajia Li
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Wavelet Frames ◽  
Dual Frames ◽  
The Past

For the past few years, wavelet and multi-wavelet frames have attracted interest from researchers. In this paper, we address some of these problems in the setting of the Sobolev space, and characterize of multi-wavelet dual frames in these spaces by using a pair of equations.

scholarly journals Dualwavelet frames in Sobolev spaces on local fields of positive characteristic

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2091-2099
Author(s):  
Ishtaq Ahmad ◽  
Neyaz Sheikh
Keyword(s):  
Sobolev Spaces ◽  
Local Field ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
The Past ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Field Of Positive Characteristic

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

scholarly journals Nonhomogeneous Wavelet Dual Frames and Extension Principles in Reducing Subspaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jianping Zhang ◽  
Huifang Jia
Keyword(s):  
Wavelet Frames ◽  
Dual Frames ◽  
Reducing Subspaces ◽  
Extension Principles

It can be seen from the literature that nonhomogeneous wavelet frames are much simpler to characterize and construct than homogeneous ones. In this work, we address such problems in reducing subspaces of L2ℝd. A characterization of nonhomogeneous wavelet dual frames is obtained, and by using the characterization, an MOEP and an MEP are derived under general assumptions for such wavelet dual frames.

The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions

2010 ◽  
Vol 439-440 ◽  
pp. 1135-1140
Author(s):  
Jun Qiu Wang ◽  
Jian Guo Wang
Keyword(s):  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
The Past ◽  
Single Function ◽  
Dual Wavelet Frames ◽  
Popular Subject ◽  
Compactly Supported Functions ◽  
Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

scholarly journals Characterization of the variable exponent Sobolev norm without derivatives

2017 ◽  
Vol 19 (03) ◽  
pp. 1650022 ◽  
Author(s):  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Sobolev Norm ◽  
Difference Quotient ◽  
Variable Exponent Sobolev Space ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.

The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
Author(s):  
R. E. Herfert
Keyword(s):  
Surface Characterization ◽  
Analytical Techniques ◽  
X Ray Diffraction ◽  
Depth Of Penetration ◽  
X Ray ◽  
The Past ◽  
Transmission Electron ◽  
Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

‘The Wretch of To-day, may be happy To-morrow’

2017 ◽  
Author(s):  
Sarah Lloyd
Keyword(s):  
Emotional Experience ◽  
The Past

This chapter explores what we can know about the conceptualization and representation of by poorer Britons. It draws on ‘pauper letters’ to parish authorities, written tactically, and on autobiographies and letters composed by the relatively poor, noting echoes of the characterization of happiness by elite social commentators. It draws attention to a growing interest (linked to the development of the concept of nostalgia) in the emotional charge that could be derived from reflection on emotional experience as people contrasted past happiness with present misery, or vice versa. While reading such accounts may lead us to think that we are penetrating the interior lives of marginal people in the past, Lloyd suggests that our response is probably coloured by the fact that we are heirs to these ways of conceptualizing and representing experience. We need to work harder to glean insight from earlier ways of representing happiness and suffering.

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