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VECTOR-VALUED WEYL–HEISENBERG WAVELET FRAME

M. K. AHMAD

Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

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and

JAVID IQBAL

Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

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https://doi.org/10.1142/S0219691309003112Cited by:2 (Source: Crossref)

Abstract

This paper deals with the theory of frames for vector-valued Weyl–Heisenberg wavelets (VVWHW). We derive frame and the corresponding frame bounds for VVWHW.

Keywords:

AMSC: 41A58, 42C15, 42C40, 65D18, 94A08

References

A. Arneodoet al., Wavelets and Applications, RMA Res. Notes Appl. Math 20, ed. Y. Meyer (Springer, 1992) pp. 286–352. Google Scholar
P. Balazs, Int. J. Wavelets Multiresolut. Inf. Process. 6(2), 315 (2008), DOI: 10.1142/S0219691308002379. Link, Web of Science, Google Scholar
Q. Chen and Z. Cheng, Chaos Solitons Fractals 31, 1024 (2007), DOI: 10.1016/j.chaos.2006.03.097. Crossref, Web of Science, Google Scholar
C. K. Chui and J.-A. Lian, Appl. Numer. Math. 20, 273 (1996), DOI: 10.1016/0168-9274(95)00111-5. Crossref, Web of Science, Google Scholar
O. Christensen, Bull. Amer. Math. Soc. 38(3), 273 (2001), DOI: 10.1090/S0273-0979-01-00903-X. Crossref, Web of Science, Google Scholar
R. R. Coifman and R. Rochberg, Asterisque 77, 11 (1980). Google Scholar
I. Daubechies, Comm. Pure Appl. Math. 41, 909 (1988), DOI: 10.1002/cpa.3160410705. Crossref, Web of Science, Google Scholar
I. Daubechies, IEEE Trans. Inform. Theory 36(5), 961 (1990), DOI: 10.1109/18.57199. Crossref, Web of Science, Google Scholar
I. Daubechies , Ten Lectures on Wavelets ( SIAM , 1992 ) . Crossref, Google Scholar
R. J. Duffin and A. C. Schaeffer, Trans. Amer. Math. Soc. 72, 341 (1952), DOI: 10.2307/1990760. Crossref, Web of Science, Google Scholar
M. Ehler, Int. J. Wavelets Multiresolut. Inf. Process. 6(2), 183 (2008), DOI: 10.1142/S0219691308002306. Link, Web of Science, Google Scholar
M. S. El Naschie, Chaos Solitons Fractals 25, 955 (2005), DOI: 10.1016/j.chaos.2004.12.033. Crossref, Web of Science, Google Scholar
M. S. El Naschie, Chaos Solitons Fractals 27, 39 (2006), DOI: 10.1016/j.chaos.2005.04.094. Crossref, Web of Science, Google Scholar
J. S. Geronimo, D. P. Hardin and P. R. Massopust, J. Approx. Theory 78(3), 373 (1994), DOI: 10.1006/jath.1994.1085. Crossref, Web of Science, Google Scholar
A. Grossmann, J. Morlet and T. Paul, J. Math. Phys. 26, 2473 (1985), DOI: 10.1063/1.526761. Crossref, Web of Science, Google Scholar
A. Grossmann, J. Morlet and T. Paul, Ann. Inst. H. Poincaré Phys. Theor. 45, 293 (1986). Web of Science, Google Scholar
C. Heil and D. Walnut, SIAM Rev. 31, 628 (1989), DOI: 10.1137/1031129. Crossref, Web of Science, Google Scholar
C. Kalisa and B. Torresani, Ann. Inst. H. Poincaré Phys. Theor. 59(2), 201 (1993). Web of Science, Google Scholar
S. Mallat, IEEE Trans. Pattern Anal. Mech. Intell. 11(7), 674 (1989), DOI: 10.1109/34.192463. Crossref, Web of Science, Google Scholar
Y. Meyer , Wavelets Algorithms and Applications ( SIAM , 1993 ) . Google Scholar
L. Sun and Z. Cheng, Chaos Solitons Fractals 34, 253 (2007), DOI: 10.1016/j.chaos.2006.06.085. Crossref, Web of Science, Google Scholar
B. Torresani, J. Math. Phys. 32(5), 1273 (1991), DOI: 10.1063/1.529325. Crossref, Web of Science, Google Scholar
B. Torresani, Ann. Inst. H. Poincaré Phys. Theor. 56(2), 215 (1992). Google Scholar
M. V. Wickerhauser, Wavelets — A Tutorial in Theory and Applications, ed. C. K. Chui (Academic Press, 1992) pp. 679–700. Google Scholar
D. Wirasael and S. Paolucci, J. Fluids Eng. 127, 656 (2005). Crossref, Web of Science, Google Scholar
X. G. Xia and B. W. Suter, IEEE Trans. Signal Process. 44(3), 508 (1996). Crossref, Web of Science, Google Scholar
X. Yang, X. Zhang and Z. Zhu, Int. J. Wavelets Multiresolut. Inf. Process. 6(3), 419 (2008), DOI: 10.1142/S0219691308002446. Link, Web of Science, Google Scholar