Wavelet Sets and Scaling Sets in Local Fields

被引：3
作者：
Behera, Biswaranjan [1 ]
机构：
[1] Stat & Math Unit, 203 BT Rd, Kolkata 700108, India
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2021年 / 27卷 / 05期
关键词：
Local field; Wavelet set; Scaling set; Generalized scaling set; MSF wavelet; MRA-wavelet; Translation congruence; Dilation congruence; MULTIRESOLUTION ANALYSIS; DIMENSION FUNCTIONS; CONSTRUCTION; DILATIONS; MRAS;
D O I：
10.1007/s00041-021-09887-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide characterizations of minimally supported frequency multiwavelets, multiwavelet sets, generalized scaling sets, and scaling sets in a local field of positive characteristic. We also construct examples of multiwavelet sets and wavelet sets. In particular, we construct examples of unbounded wavelet sets and show that the corresponding wavelets are not associated with multiresolution analyses.
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页数：23
相关论文
共 40 条
[1]  
Arcozzi N., 2003, J GEOM ANAL, V13, P557, DOI [10.1007/BF02921878, DOI 10.1007/BF02921878]
[2]   Generalized multi-resolution analyses and a construction procedure for all wavelet sets in Rn [J].
Baggett, LW ;
Medina, HA ;
Merrill, KD .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1999, 5 (06) :563-573
[3]   Estimation of dimension functions of band-limited wavelets [J].
Behera, B .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2002, 13 (03) :277-282
[4]  
Behera B., 2005, J CONCR APPL MATH, V3, P75
[5]  
Behera B., 2004, Bull. Pol. Acad. Sci. Math, V52, P169, DOI DOI 10.4064/BA52-2-7
[6]   Characterization of wavelets and MRA wavelets on local fields of positive characteristic [J].
Behera, Biswaranjan ;
Jahan, Qaiser .
COLLECTANEA MATHEMATICA, 2015, 66 (01) :33-53
[7]   Multiresolution analysis on local fields and characterization of scaling functions [J].
Behera, Biswaranjan ;
Jahan, Qaiser .
ADVANCES IN PURE AND APPLIED MATHEMATICS, 2012, 3 (02) :181-202
[8]  
Benedetto J., 1999, FUNCTIONAL HARMONIC, P43
[9]  
Benedetto JJ, 2001, J GEOM ANAL, V11, P1
[10]   A wavelet theory for local fields and related groups [J].
Benedetto, JJ ;
Benedetto, RL .
JOURNAL OF GEOMETRIC ANALYSIS, 2004, 14 (03) :423-456
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