Volume 49 | Number 3 | Year 2017 | Article Id. IJMTT-V49P527 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P527
P.Kalyani, "Frames and its applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 3, pp. 188-194, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P527
Different types of frames and operators are defined with examples and applications of each of the type of frames are explained.
[1] M.R.Abdollahpour ,M.H. Faroughi and A.Rahimi ,”PG-Frames in Banach spaces” Methods of Functional analysis and topology Vol.13 NO.3(2007),pp.201-210.
[2] R.BalanP.G.Casazza, D.Edidin and G.Kutynoik “ Decomopostion of frames and a new frame identity “ Wavelet XI (San Diego),CA(2005) pp.379-388 SPIE Proc 5914 ,SPIE Bellinginam WA.
[3] P.G.Casazza,The art of Frame theory Taiwanese Journal of Mathematics Vol.4,No.2(2000) pp 129-201.
[4] D.Han and D.R.Larson “Frames Bases and Group Representations” Memories Ams Nov 7 (2000) Providence RI.
[5] A.Najati and A.Rahimi “Generalized frames in Hilbert spaces” Bulletin of the Iranian Mathematical society Vol.35,No.1(2009) pp.97-109.
[6] A.Najati and M.H.Faroughi “P- frames of subspaces of separable Hilbert spaces South east AsainBulletion of Mathematics 31(2007)pp.713-726.
[7] G. Upender Reddy and N.Gopal Reddy ,Some results of Frame operator in Hilbert space, Journal of Mathematical education ,Volume XLV,No.3 September 2011.
[8]. Helmut Bolcskei ,Franz Hlawatsuh and Hans G.Feicgitinger ,” Frame –Theoretic analysis and design of oversampled filter banks “.In proc ,IEEE ISCAS 1996 .Atlanta ,GA,Vol 2 ,PP,409 -412 ,may 1996.
[9] . Helmut Bolcskei ,Franz Hlawatsuh and Hans G.Feicgitinger “Frame –Theoretic analysis of oversampled filter banks”,IEEE Trasactions and signal processing ,Vol 4,No 12,1998.
[10] . G.Upender Reddy and N. Gopal Reddy „A Note on Frame Potential in Finite Dimensional Hilbert Space‟, Journal of Indian Academy of Mathematics, Volume. 32, No.1, 2010.
[11]. G.Upender Reddy and N. Gopal Reddy ,A brief study of multi frames and super frames in Hilbert spaces”Journal of ultra scentist of physical sciences ,vol.20 (2)m,Aug 2008,501-510.
[12]. Zoran Cvetkoric and martin Votter li,”Over Sampled Filter banks ,IEEE Transaction on signal processing ,Vol 46 ,No 5,May 1998.
[13] I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory, vol. 36, pp. 961–1005, Sep. 1990.
[14] Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, 1992.
[15] C. E. Heil and D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev., vol. 31, pp. 628–666, Dec. 1989.
[16] R. M. Young, An Introduction to Nonharmonic Fourier Series. New York: Academic Press, 1980.
[17] D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613–627, Mar. 1995.
[18] D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika, vol. 81, no. 3, pp. 425–455, Aug. 1994.
[19] M. Rupf and J. L. Massey, “Optimum sequence multisets for synchronous code-division multipleaccess channels,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1261–1266, Jul. 1994.
[20] M. Sandell, “Design and analysis of estimators for multicarrier modulation and ultrasonic imaging,” Ph.D. dissertation, Lule˚a Univ. Technol., Lule˚a, Sweden, Sep. 1996.
[21] R. W. Heath, Jr. and A. J. Paulraj, “Linear dispersion codes for MIMO systems based on frame theory,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 2429–2441, Oct. 2002.
[22] M. Rudelson and R. Vershynin, “Geometric approach to error correcting codes and reconstruction.