Construction of MRA and non-MRA wavelet sets on Cantor dyadic group

Author(s):  
Prasadini Mahapatra ◽  
Divya Singh
Author(s):  
Prasadini Mahapatra ◽  
Divya Singh

Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group [Formula: see text]. These results can further be generalized to arbitrary locally compact abelian groups.


1998 ◽  
Vol 21 (2) ◽  
pp. 307-314 ◽  
Author(s):  
W. Christopher Lang

Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double-knot spline spaceS1,2.


2000 ◽  
Vol 129 (7) ◽  
pp. 2045-2055 ◽  
Author(s):  
X. Dai ◽  
Y. Diao ◽  
Q. Gu
Keyword(s):  

2003 ◽  
Vol 155 (1) ◽  
pp. 69-82 ◽  
Author(s):  
X. Dai ◽  
Y. Diao ◽  
Q. Gu ◽  
D. Han
Keyword(s):  

2013 ◽  
Vol 4 (2) ◽  
pp. 71-103 ◽  
Author(s):  
Richard L. Lanigan

Communicology is the science of human communication where consciousness is constituted as a medium of communication at four interconnected levels of interaction experience: intrapersonal (embodied), interpersonal (dyadic), group (social), and inter-group (cultural). The focus of the paper is the group level of communication across generations, thus constituting inter-group communication that stabilizes norms (forms a culture). I propose to explicate the way in which the method of semiotic phenomenology informs the pioneering work at the University of Toronto by Tom McFeat, a Harvard trained cultural anthropologist, on small group cultures as an experimental research methodology. Rather than the cognitiveanalytic (Husserl‘s transcendental eidetic) techniques suggest by Don Ihde as a pseudo "experimental phenomenology", McFeat provides an applied method for the empirical experimental constitution of culture in conscious experience. Group cultures are constructed in the communicological practices of group formation and transformation by means of a selfgenerating group narrative (myth) design. McFeat‘s method consists of three steps of culture formation by communication that are: (1) Content-Ordering, (2) Task-Ordering, and (3) Group-Ordering, i.e., what Ernst Cassirer and Karl Jaspers call the logic of culture or Culturology. These steps are compared to the descriptive phenomenology research procedures suggested by Amedeo Giorgi following Husserl‘s approach: (1) Find a sense of the whole, (2) Determine meaning units, (3) Transform the natural attitude expressions into phenomenologically, psychologically sensitive expressions. A second correlation will be made to Richard Lanigan‘s semiotic phenomenology method following the work of Cassirer, Jaspers, and Merleau-Ponty: (1) Description of Signs, (2) Reduction of Signifiers, and (3) Interpretation of Signifieds.


2011 ◽  
Vol 63 (3) ◽  
pp. 689-720
Author(s):  
Sean Olphert ◽  
Stephen C. Power

Abstract A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in L2(ℝd). While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct Latin square wavelets as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.


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