Multiresolution Analysis of Function Spaces

2020 ◽  
pp. 22-49
Author(s):  
M M Panja ◽  
B N Mandal
Keyword(s):  
Multiresolution Analysis ◽  
Function Spaces ◽  
Analysis Of Function

scholarly journals Quaternionic Blaschke Group

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 33
Author(s):  
Margit Pap ◽  
Ferenc Schipp
Keyword(s):  
Analytic Function ◽  
Multiresolution Analysis ◽  
Function Spaces ◽  
Complex Case ◽  
Wavelet Theory ◽  
Variable Function ◽  
Analytic Function Spaces

In the complex case, the Blaschke group was introduced and studied. It turned out that in the complex case this group plays important role in the construction of analytic wavelets and multiresolution analysis in different analytic function spaces. The extension of the wavelet theory to quaternion variable function spaces would be very beneficial in the solution of many problems in physics. A first step in this direction is to give the quaternionic analogue of the Blaschke group. In this paper we introduce the quaternionic Blaschke group and we study the properties of this group and its subgroups.

Multiresolution analysis for compactly supported interpolating tensor product wavelets

2015 ◽  
Vol 13 (02) ◽  
pp. 1550010 ◽  
Author(s):  
Tommi Höynälänmaa
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Multiresolution Analysis ◽  
Continuous Functions ◽  
Function Spaces ◽  
One Dimensional ◽  
Space Norm ◽  
The One ◽  
Complex Valued ◽  
Uniformly Continuous

We construct multidimensional interpolating tensor product multiresolution analyses (MRA's) of the function spaces C0(ℝn, K), K = ℝ or K = ℂ, consisting of real or complex valued functions on ℝn vanishing at infinity and the function spaces Cu(ℝn, K) consisting of bounded and uniformly continuous functions on ℝn. We also construct an interpolating dual MRA for both of these spaces. The theory of the tensor products of Banach spaces is used. We generalize the Besov space norm equivalence from the one-dimensional case to our n-dimensional construction.

Driver's Mental Stress Visualization by Discrete Wavelet Multiresolution Analysis.

2000 ◽  
Vol 20 (79) ◽  
pp. 356-364
Author(s):  
Taro SEKINE ◽  
Masahiro TAKEI ◽  
Michiharu OKANO ◽  
Hiroyasu NAGAE ◽  
Yoshifuru SAITO ◽  
...  
Keyword(s):  
Multiresolution Analysis ◽  
Mental Stress ◽  
Discrete Wavelet ◽  
Wavelet Multiresolution Analysis

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces
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