پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شمارهها | 438 |
| تعداد مقالات | 5,650 |
| تعداد مشاهده مقاله | 7,683,871 |
| تعداد دریافت فایل اصل مقاله | 6,340,088 |
Pseudo-duals and closeness of continuous g-frames in Hilbert spaces | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 7، شماره 1، فروردین 2026، صفحه 33-44 اصل مقاله (423.63 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.23279.1247 | ||
| نویسندگان | ||
| Morteza Mirzaee Azandaryani* ؛ Zeinab Javadi | ||
| Department of Mathematics, University of Qom, Qom, Iran | ||
| چکیده | ||
| The paper deals with pseudo-duals of continuous $g$-frames and their characterizations in Hilbert spaces. Mainly, the pseudo-duals constructed by bounded operators inserted between the synthesis and analysis operators of the Bessel mappings are considered. Duals and approximate duals, which are two important classes of pseudo-duals, are also studied here. Moreover, the concepts of closeness and nearness of continuous $g$-frames are focused and some of their properties are obtained. It is shown that there are close relationships between the closeness and nearness of $g$-frames and their approximate duals. Also, the above-mentioned concepts are related to the notions of partial equivalence, equivalent frames, and continuous Riesz-type $g$-frames. | ||
| کلیدواژهها | ||
| Hilbert space؛ Continuous $g$-frame؛ Pseudo-dual؛ Approximate dual؛ The closeness of $g$-frames؛ The nearness of $g$-frames | ||
| مراجع | ||
|
[1] M. R. Abdollahpour and M. H. Faroughi, Continuous G-frames in Hilbert spaces, Southeast Asian Bull. Math., 32 (2008), pp. 1–19.
[2] S. T. Ali, J.-P. Antoine, and J.-P. Gazeau, Continuous frames in Hilbert space, Ann. Physics, 222 (1993), pp. 1–37.
[3] Z. Amiri and R. A. Kamyabi-Gol, Distance between continuous frames in Hilbert space, J. Korean Math. Soc., 54 (2017), pp. 215–225.
[4] M. M. Azandaryani and Z. Javadi, Pseudo-duals of continuous frames in Hilbert spaces, J. Pseudo-Differ. Oper. Appl., 13 (2022), pp. Paper No. 52, 16.
[5] R. Balan, Equivalence relations and distances between Hilbert frames, Proc. Amer. Math. Soc., 127 (1999), pp. 2353–2366.
[6] O. Christensen, Frame perturbations, Proc. Amer. Math. Soc., 123 (1995), pp. 1217–1220.
[7] , A Paley-Wiener theorem for frames, Proc. Amer. Math. Soc., 123 (1995), pp. 2199–2201.
[8] , Frames and bases, Applied and Numerical Harmonic Analysis, Birkh¨auser Boston, Inc., Boston, MA, 2008. An introductory course.
[9] O. Christensen and R. S. Laugesen, Approximately dual frames in Hilbert spaces and applications to Gabor frames, Sampling Theory in Signal and Image Processing, 9 (2010), pp. 77–89.
[10] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271–1283.
[11] Deepshikha, Equivalence relations and distances between generalized frames, J. Pseudo-Differ. Oper. Appl., 13 (2022), pp. Paper No. 47, 19.
[12] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952), pp. 341–366.
[13] J.-P. Gabardo and D. Han, Frames associated with measurable spaces, Adv. Comput. Math., 18 (2003), pp. 127–147. Frames.
[14] S. B. Heineken, P. M. Morillas, A. M. Benavente, and M. I. Zakowicz, Dual fusion frames, Arch. Math. (Basel), 103 (2014), pp. 355–365.
[15] G. Kaiser, A friendly guide to wavelets, Birkh¨auser Boston, Inc., Boston, MA, 1994.
[16] A. Khosravi and M. Mirzaee Azandaryani, Approximate duality of g-frames in Hilbert spaces, Acta Math. Sci. Ser. B (Engl. Ed.), 34 (2014), pp. 639–652.
[17] H. Massit, M. Rossafi, and C. Park, Some relations between continuous generalized frames, Afr. Mat., 35 (2024), pp. Paper No. 12, 14.
[18] M. Mirzaee Azandaryani, On the approximate duality of g-frames and fusion frames, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 79 (2017), pp. 83–94.
[19] , An operator theory approach to the approximate duality of Hilbert space frames, J. Math. Anal. Appl., 489 (2020), pp. 124177, 13.
[20] A. Rahimi, Z. Darvishi, and B. Daraby, Dual pair and approximate dual for continuous frames in Hilbert spaces, Math. Rep. (Bucur.), 21(71) (2019), pp. 173–191.
[21] A. Razghandi and A. A. Arefijamaal, On the characterization of generalized dual frames, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 82 (2020), pp. 161–170.
[22] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437–452.
[23] X. Xiao, G. Zhao, and G. Zhou, Q-duals and Q-approximate duals of g-frames in Hilbert spaces, Numer. Funct. Anal. Optim., 44 (2023), pp. 510–528.
[24] R. M. Young, An introduction to nonharmonic Fourier series, vol. 93 of Pure and Applied Mathematics, Academic Press, Inc., New York-London, 1980.
[25] A. Yousefzadeheyni and M. R. Abdollahpour, Some properties of approximately dual continuous g- frames in Hilbert spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 82 (2020), pp. 183–194. | ||
|
آمار تعداد مشاهده مقاله: 336 تعداد دریافت فایل اصل مقاله: 72 |
||