Year 2017,
Volume: 7 Issue: 2, 200 - 208, 01.12.2017
Abstract
Cordoba and Fe erman [4] introduced wave packet systems by applying certain collections of dilations, modulations and translations to the Gaussian function in the study of some classes of singular integral operators. In this paper, we introduce the concept of matrix transform M = p;q;r;j;k;m and with the help of matrix transform we study the action of M on f 2 L2 R and on its wave packet coecients. Further, we also obtain the tight frame condition for matrix transform of f 2 L2 R whose wave packet series expansion is known.
Keywords
References
- Casazza,P.G. and Kutyniok,G., (2012), Finite frames: Theory and Applications, Birkh¨auser.
- Christensen,O. and Rahimi,A., (2008), Frame properties of wave packet systems in L2(R), Adv. Com- put. Math., 29, pp.101-111.
- Christensen,O., (2008), Frames and Bases, An Introductory Course, Birkh¨auser, Boston.
- Cordoba,A. and Fefferman,C., (1978), Wave packets and Fourier integral operators, Comm. Partial Differential Equations, 3, 11, pp.979-1005.
- Czaja,W., Kutyniok,G., and Speegle,D., (2006), The Geometry of sets of prameters of wave packets, Appl. Comput. Harmon. Anal., 20, pp.108-125.
- Duffin,R.J. and Schaeffer,A.C., (1952), A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, pp.341-366.
- Heil,C., (2011), A Basis Theory Primer, Expanded edition, Applied and Numerical Harmonic Analysis, Birkh¨auser/Springer, New York.
- Hern´andez,E., Labate,D., Weiss,G.,and Wilson,E., (2004), Oversampling, quasi-affine frames and wave packets, Appl. Comput. Harmon. Anal., 16, pp.111-147.
- Labate,D., Weiss,G.,and Wilson,E., (2004), An approach to the study of wave packet systems, Con- temp. Math., 345, pp.215-235.
- Sah,A.K.,and Vashisht,L.K., (2015), Irregular Weyl-Heisenberg wave packet frames in L2(R), Bull.Sci. Math., 139, pp.61-74.
- Young,R., (2001), An introduction to nonharmonic Fourier series, Academic Press, New York.
Year 2017,
Volume: 7 Issue: 2, 200 - 208, 01.12.2017
Abstract
References
- Casazza,P.G. and Kutyniok,G., (2012), Finite frames: Theory and Applications, Birkh¨auser.
- Christensen,O. and Rahimi,A., (2008), Frame properties of wave packet systems in L2(R), Adv. Com- put. Math., 29, pp.101-111.
- Christensen,O., (2008), Frames and Bases, An Introductory Course, Birkh¨auser, Boston.
- Cordoba,A. and Fefferman,C., (1978), Wave packets and Fourier integral operators, Comm. Partial Differential Equations, 3, 11, pp.979-1005.
- Czaja,W., Kutyniok,G., and Speegle,D., (2006), The Geometry of sets of prameters of wave packets, Appl. Comput. Harmon. Anal., 20, pp.108-125.
- Duffin,R.J. and Schaeffer,A.C., (1952), A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, pp.341-366.
- Heil,C., (2011), A Basis Theory Primer, Expanded edition, Applied and Numerical Harmonic Analysis, Birkh¨auser/Springer, New York.
- Hern´andez,E., Labate,D., Weiss,G.,and Wilson,E., (2004), Oversampling, quasi-affine frames and wave packets, Appl. Comput. Harmon. Anal., 16, pp.111-147.
- Labate,D., Weiss,G.,and Wilson,E., (2004), An approach to the study of wave packet systems, Con- temp. Math., 345, pp.215-235.
- Sah,A.K.,and Vashisht,L.K., (2015), Irregular Weyl-Heisenberg wave packet frames in L2(R), Bull.Sci. Math., 139, pp.61-74.
- Young,R., (2001), An introduction to nonharmonic Fourier series, Academic Press, New York.
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 1, 2017 |
| Published in Issue | Year 2017 Volume: 7 Issue: 2 |