Volume 15, Issue 2 (10-2020)
IJMSI 2020, 15(2): 1-12 |
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Abdollahpour M R, Najati A, Gavruta P. Multipliers of pg-Bessel sequences in Banach spaces. IJMSI 2020; 15 (2) :1-12
URL: http://ijmsi.ir/article-1-802-en.html
URL: http://ijmsi.ir/article-1-802-en.html
Abstract:
In this paper, we introduce $(p,q)g-$Bessel multipliers in Banach spaces and we show that under some conditions a $(p,q)g-$Bessel multiplier is invertible. Also, we show the continuous dependency of $(p,q)g-$Bessel multipliers on their parameters.
Type of Study: Research paper |
Subject:
Special
References
1. M. R. Abdollahpour, M. H. Faroughi, A. Rahimi, pg-Frames in Banach spaces, textit{ Methods Func. Anal.Topology}, textbf{135}(3), (2007), 201--210.
2. C. D. Aliprantis, K. C. Border, textit{ Infinite dimensional analysis}, Springer, 1999. [DOI:10.1007/978-3-662-03961-8]
3. A. Aldroubi, Q. Sung, W. Tang, $p-$frames and shift invariant subspaces of $L^p$, textit{J. Fourier Anal. Appl.}, textbf{7}, (2001), 1-22. [DOI:10.1007/s00041-001-0001-2]
4. P. Balazs, Basic definition and properties of Bessel multipliers, textit{J. Math. Anal. and Appl.}, textbf{325}(1), (2007), 571-585. [DOI:10.1016/j.jmaa.2006.02.012]
5. P. Balazs, Hilbert-Schmidt operators and frames-classifications, approximation by multipliers and algorithms, textit{Int. J. Wavelets, Multiresolut. Inf. Process.}, textbf{6}(2), (2008), 315-330. [DOI:10.1142/S0219691308002379]
6. P. Balazs, D. Stoeva, Representation of the inverse of a multiplier, textit{J. Math. Anal. Appl.}, textbf{422}(2), (2015), 981-994. [DOI:10.1016/j.jmaa.2014.09.020]
7. O. Christensen, textit{An Introduction to Frames and Riesz Bases}, Birkha" user, 2003. [DOI:10.1007/978-0-8176-8224-8]
8. O. Christensen, D. Stoeva, p-Frames in separable Banach spaces, textit{ Adv. Comput. Math.}, textbf{18}, (2003), 117-126. [DOI:10.1023/A:1021364413257]
9. R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, textit{Trans. Amer. Math. Soc.},textbf{72}, (1952), 341-366. [DOI:10.1090/S0002-9947-1952-0047179-6]
10. H. G. Feichtinger, K. Gr"ochenig, A unified approach to atomic decompositions via integrable group representations, In: Proc. Conf. textit{Function Spaces and Applications}.(M. Cwikel et al. eds.), 52-73. Lect. Notes Math 1302. Berlin-Heidelberg-New York: Springer, 1988. [DOI:10.1007/BFb0078863]
11. K. Grochenig, Describing functions: atomic decompositions versus frames, textit{Monatsh. Math}, textbf{112}, (1991), 1-41. [DOI:10.1007/BF01321715]
12. A. Rahimi, Multipliers of Generalized Frames in Hilbert spaces, textit{Bull. Iranian Math. Soc.}, textbf{37}(1), (2011), 63-80.
13. A. Rahimi, P. Balazs, Multipliers for p-Bessel sequences in Banach spaces, textit{Integr. Equ. Oper. Theory}, textbf{68}, (2010), 193-205, DOI: 10.1007/s00020-010-1814-7. [DOI:10.1007/s00020-010-1814-7]
14. M.B. Ruskai, Some connections between frames,mutually unbiased bases, and POVM s in Quantum Information Theory, textit{Acta Appl.Math.}, textbf{108}(3), (2009), 709-719. [DOI:10.1007/s10440-009-9508-3]
15. D. Stoeva, P. Balazs, Invertibility of Multipliers, textit{Applied and Computational Harmonic Analysis}, textbf{33}(2), (2012), 292-299. [DOI:10.1016/j.acha.2011.11.001]
16. D. Stoeva, P. Balazs, Canonical forms of unconditionally convergent multipliers, textit{J. Math. Anal. Appl.}, textbf{399}, (2013), 252-259. [DOI:10.1016/j.jmaa.2012.10.007]
17. D. Stoeva, P. Balazs, Detailed characterization of unconditional convergence and invertibility of multipliers, textit{Sampling Theory in Signal and Image Processing (STSIP)}, textbf{12}(2), (2013), 87-125.
18. W. Sun, g-Frames, g-Riesz bases, textit{J. Math. Anal. Appl}, textbf{322}(1), (2006), 437-452. [DOI:10.1016/j.jmaa.2005.09.039]
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