Research Article
Year 2020,
Volume: 49 Issue: 3, 1057 - 1066, 02.06.2020
Abstract
In this paper, the concept of $K$-pseudoframes for subspaces of Hilbert spaces, as a generalization of both $K$-frames and pseudoframes, is introduced and some of their properties and their characterizations are investigated. Next, duals of $K$-pseudoframes are discussed. Finally, the concept of pseudoatomic system is introduced and its relations with $K$-pseudoframe are studied.
References
- [1] F. Arabyani Neyshaburi and A.A. Arefijamaal, Some constructions of K-frames and their duals, Rocky Mountain J. Math. 47 (6), 1749–1764, 2017.
- [2] P.G. Casazza and G. Kutyniok, Frames of subspaces. Wavelets, frames and operator theory, College Park, MD, Contempt. Math. 345, American Mathematical Society, Providence, 87–113, 2004.
- [3] P.G. Casazza and S. Li, Fusion frames and distributed processing, App. Comput. Harmon. Anal. 25, 114–132, 2008.
- [4] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27, 1271–1283, 1986.
- [5] R.G. Douglas On majoration, factorization and range inclusion for operators on Hilbert spaces, Proc. Amer. Math. Soc. 17 (2), 413–415, 1966.
- [6] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Math. Soc. 72, 341–366, 1952.
- [7] L. Găvruţa, Frames for operators, Appi. Comput. Harmon. Anal. 32, 139–144, 2012.
- [8] L. Găvruţa, New results on operators, Anal. Univ. Oradea, Fasc. Mat. 19, 55–61, 2012.
- [9] L. Găvruţa, Atomic decompositions for operators in reproducing kernel Hilbert spaces, Math. Reports. 17 (67-3), 303–314, 2015.
- [10] S. Li, A theory of generalized multiresolution structure and pseudoframes of translation, J. Fourier Anal. Appl. 7 (1), 23–40, 2001.
- [11] S. Li and H. Ogawa, A theory of pseudoframes for subspaces with applications, Tokyo Institute of Technology, Technical Report, 1998.
- [12] W.C. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, 437–452, 2006.
- [13] X. Xiao, Y. Zhu and L. Găvruţa, Some properties of K-frames in Hilbert spaces, Results Math. 63, 1243–1255, 2013.
Year 2020,
Volume: 49 Issue: 3, 1057 - 1066, 02.06.2020
Abstract
References
- [1] F. Arabyani Neyshaburi and A.A. Arefijamaal, Some constructions of K-frames and their duals, Rocky Mountain J. Math. 47 (6), 1749–1764, 2017.
- [2] P.G. Casazza and G. Kutyniok, Frames of subspaces. Wavelets, frames and operator theory, College Park, MD, Contempt. Math. 345, American Mathematical Society, Providence, 87–113, 2004.
- [3] P.G. Casazza and S. Li, Fusion frames and distributed processing, App. Comput. Harmon. Anal. 25, 114–132, 2008.
- [4] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27, 1271–1283, 1986.
- [5] R.G. Douglas On majoration, factorization and range inclusion for operators on Hilbert spaces, Proc. Amer. Math. Soc. 17 (2), 413–415, 1966.
- [6] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Math. Soc. 72, 341–366, 1952.
- [7] L. Găvruţa, Frames for operators, Appi. Comput. Harmon. Anal. 32, 139–144, 2012.
- [8] L. Găvruţa, New results on operators, Anal. Univ. Oradea, Fasc. Mat. 19, 55–61, 2012.
- [9] L. Găvruţa, Atomic decompositions for operators in reproducing kernel Hilbert spaces, Math. Reports. 17 (67-3), 303–314, 2015.
- [10] S. Li, A theory of generalized multiresolution structure and pseudoframes of translation, J. Fourier Anal. Appl. 7 (1), 23–40, 2001.
- [11] S. Li and H. Ogawa, A theory of pseudoframes for subspaces with applications, Tokyo Institute of Technology, Technical Report, 1998.
- [12] W.C. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, 437–452, 2006.
- [13] X. Xiao, Y. Zhu and L. Găvruţa, Some properties of K-frames in Hilbert spaces, Results Math. 63, 1243–1255, 2013.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 2, 2020 |
| Published in Issue | Year 2020 Volume: 49 Issue: 3 |