Stability and Perturbations of Chi-Phi Frame in Banach Spaces
DOI:
https://doi.org/10.54060/a2zjournals.jase.112Keywords:
Stability, Analysis operator, PerturbationsAbstract
Frames in relation to certain sequence spaces, specifically Chi-Phi frames, were introduced and studied. Further investigations into Chi-Phi frames and their various characterizations can be found. The stability and perturbation of frames are crucial in practical applications and have been extensively studied. In this paper, we examine the stability and perturbations of Chi-Phi frames and Chi-Phi Bessel sequences in Banach spaces, extending two important propositions from [3]and [7], respectively.
Downloads
References
P. G. Casazza, O. Cristenson, and D. T. Stoeva, “Frames expansions in separable Banach spaces,” J. Math.,Anal. Appl, vol. 307, no. 2, pp. 710–723, 2005.
P. G. Casazza, D. Han, and D. R. Larson, “Frames for Banach spaces, Contemp,” Contemp. Math, vol. 247, pp. 149–182, 1999.
P. G. Casazza and O. Christensen, “Perturbation of operators and applications to frame theory,” J. Fourier Anal. Appl, vol. 3, no. 5, pp. 543–557, 1997.
O. Christensen and D. T. Stoeva, “-Frames in separable Banach spaces, Adv,” Adv. Comput.Math, vol. 18, no. 2, pp. 117–126, 2003.
O. Christensen and C. Heil, “Perturbations of Banach frames and atomic decompositions: Perturbations of frames,” Math. Nachr., vol. 185, no. 1, pp. 33–47, 1997.
O. Christensen, “An itroduction to frames and Riesz bases,” Appl. Numer. Harmon. Anal, 1992.
O. Christensen, “Frame perturbation,” Proc. Amer. Math. Soc., vol. 123, no. 4, pp. 1217-1220, 1995.
R. J. Duffin and A. C. Schaeffer, “A class of non-harmonic Fourier series,” Trans. Amer. Math. Soc, vol. 72, pp. 341–366, 1952.
H. G. Feichinger and K. Gröchenig, “A unified approach to atomic decompositions via integrable group representations,” in Proc. Conf. ``Function Spaces and Applications, vol. 1302, Berlin - Heidelberg - New York: Springer, pp. 52–73, 1988.
D. Gabor, “Theory of communications,” J.I.E.E(London), vol. 93, no. 3, pp. 429–457, 1946.
K. Gröchenig, “Describing functions., Atomic decompositions versus frames,” Monatsh. Math, vol. 112, pp. 1–41, 1991.
D. Han and D. R. Larson, “Frames, bases and group representation for Banach space,” Memoirs, Amer. Math. Soc, vol. 147, pp. 1–91, 2000.
P. K. Jain, S. K. Kaushik, and L. K. Vashisht, “On stability of Banach frames, Bull,” Bull. Korean Math, vol. 37, no. 112, pp. 1–41, 2001.
P. K. Jain, S. K. Kaushik, and L. K. Vashisht, “On stability of Banach frames, Bull,” Bull. Korean Math, vol. 37, no. 112, pp. 1–41, 2001.
M. Joshi, R. Kumar, and R. Singh, “On a weighted retro Banach frames for discrete signal spaces,” Br. J. Math. Comput. Sci., vol. 4, no. 23, pp. 3334–3344, 2014.
R. Kumar, M. C. Joshi, R. B. Singh, and A. K. Sah, “Construction of generalized atomic decomposi-tions in Banach spaces,” Int. J. Adv. Math. Sci, vol. 2, no. 3, pp. 116–124, 2014.
A. K. Sabherwal, R. B. Singh, and R. Kumar, “A note on -frame in Banach spaces,” Advances in Theoretical and Applied Mathematics, vol. 11, no. 4, pp. 495–504, 1016.
I. Singer, “Bases in Banach spaces-II,” Springer, New York, 1970.
R. B. Singh, M. Joshi, and A. K. Sah, “A note on -frames in Banach spaces,” Int. J. Math. Arch, vol. 5, no. 3, pp. 1–6, 2014.
R. B. Singh, On Generalizations of frames in Banach spaces. Nainital, India, 2014.
W. Sun, Stability of g-frames,” J. Maths Anal. Appl., vol. 326, pp. 858-868, 2007..
R. M. Young, An Introduction to Non-harmonic Fourier series. New York: Academic Press, 1980.
Downloads
Published
How to Cite
CITATION COUNT
Issue
Section
License
Copyright (c) 2025 Ram Bharat Singh, Sandeep Kumar, Anil Kumar
This work is licensed under a Creative Commons Attribution 4.0 International License.
