Wave packet systems on local fields
In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet system...
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| Published in | Journal of geometry and physics Vol. 120; pp. 5 - 18 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.10.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0393-0440 1879-1662 |
| DOI | 10.1016/j.geomphys.2017.05.015 |
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| Abstract | In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet systems in L2(K) which include the corresponding results of wavelet analysis and Gabor theory as the special cases. We shall also provide a sufficient condition of the completeness of wave packet systems on local fields of positive characteristic subject to some mild conditions. The paper concludes with the necessary and sufficient conditions for the wave packet systems to be wave packet Parseval frames for L2(K). |
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| AbstractList | In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet systems in L2(K) which include the corresponding results of wavelet analysis and Gabor theory as the special cases. We shall also provide a sufficient condition of the completeness of wave packet systems on local fields of positive characteristic subject to some mild conditions. The paper concludes with the necessary and sufficient conditions for the wave packet systems to be wave packet Parseval frames for L2(K). |
| Author | Ahmad, Owais Shah, Firdous A. |
| Author_xml | – sequence: 1 givenname: Firdous A. orcidid: 0000-0001-8461-869X surname: Shah fullname: Shah, Firdous A. email: fashah79@gmail.com organization: Department of Mathematics, University of Kashmir, South Campus, Anantnag-192 101, Jammu and Kashmir, India – sequence: 2 givenname: Owais surname: Ahmad fullname: Ahmad, Owais email: siawoahmad@gmail.com organization: Department of Mathematics, National Institute of Technology, Hazratbal Srinagar-190006, Jammu and Kashmir, India |
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| Cites_doi | 10.1007/s11425-007-2058-0 10.1360/04ys0143 10.1524/anly.2013.1217 10.1080/10652469.2010.546623 10.1007/s10444-007-9038-3 10.1063/1.527388 10.1080/10652469.2010.520528 10.1007/s11401-005-0389-0 10.1090/S0002-9947-1952-0047179-6 10.11650/tjm.18.2014.4195 10.1016/j.jmaa.2008.04.031 10.2298/FIL1706491S 10.1080/01630563.2016.1144069 10.1137/0524017 10.3103/S1068362312050056 10.7153/jca-06-07 10.1090/conm/345/06250 10.3103/S1068362314060016 10.1080/03605307808820083 |
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| References | Daubechies, Grossmann, Meyer (b3) 1986; 27 Shah, Bhat (b22) 2017; 31 Shah, Bhat (b23) 2016; 36 Shah, Abdullah (b20) 2014; 49 Shah (b7) 2012; 47 Shi, Chen (b8) 2007; 50 Chui, Shi (b4) 1993; 24 Labate, Weiss, Wilson (b12) 2004; 345 Christensen, Rahimi (b13) 2008; 29 Li, Jiang (b19) 2008; 345 Shah (b21) 2016; 37 Duffin, Shaeffer (b2) 1952; 72 Taibleson (b27) 1975 Shah, Debnath (b15) 2011; 22 Shah, Debnath (b9) 2011; 22 Shah, Abdullah (b26) 2014; 249 Debnath, Shah (b6) 2015 Li, Jiang (b18) 2007; 28 Shah, Bhat (b24) 2015; 6 Shah, Abdullah (b14) 2012; 36 Wu, Li (b16) 2014; 18 Shah, Debnath (b25) 2013; 33 Daubechies (b5) 1992 Gabor (b1) 1946; 93 Wu, Li, Cao (b17) 2014; 37 Shi, Chen (b10) 2005; 48 Córdoba, Fefferman (b11) 1978; 3 Taibleson (10.1016/j.geomphys.2017.05.015_b27) 1975 Chui (10.1016/j.geomphys.2017.05.015_b4) 1993; 24 Christensen (10.1016/j.geomphys.2017.05.015_b13) 2008; 29 Labate (10.1016/j.geomphys.2017.05.015_b12) 2004; 345 Wu (10.1016/j.geomphys.2017.05.015_b16) 2014; 18 Li (10.1016/j.geomphys.2017.05.015_b18) 2007; 28 Shah (10.1016/j.geomphys.2017.05.015_b22) 2017; 31 Duffin (10.1016/j.geomphys.2017.05.015_b2) 1952; 72 Daubechies (10.1016/j.geomphys.2017.05.015_b5) 1992 Shah (10.1016/j.geomphys.2017.05.015_b14) 2012; 36 Daubechies (10.1016/j.geomphys.2017.05.015_b3) 1986; 27 Shah (10.1016/j.geomphys.2017.05.015_b25) 2013; 33 Córdoba (10.1016/j.geomphys.2017.05.015_b11) 1978; 3 Shah (10.1016/j.geomphys.2017.05.015_b24) 2015; 6 Shah (10.1016/j.geomphys.2017.05.015_b20) 2014; 49 Shah (10.1016/j.geomphys.2017.05.015_b7) 2012; 47 Shi (10.1016/j.geomphys.2017.05.015_b8) 2007; 50 Shah (10.1016/j.geomphys.2017.05.015_b9) 2011; 22 Shah (10.1016/j.geomphys.2017.05.015_b15) 2011; 22 Li (10.1016/j.geomphys.2017.05.015_b19) 2008; 345 Gabor (10.1016/j.geomphys.2017.05.015_b1) 1946; 93 Wu (10.1016/j.geomphys.2017.05.015_b17) 2014; 37 Shi (10.1016/j.geomphys.2017.05.015_b10) 2005; 48 Shah (10.1016/j.geomphys.2017.05.015_b23) 2016; 36 Debnath (10.1016/j.geomphys.2017.05.015_b6) 2015 Shah (10.1016/j.geomphys.2017.05.015_b26) 2014; 249 Shah (10.1016/j.geomphys.2017.05.015_b21) 2016; 37 |
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