Phase Retrieval and Norm Retrieval in Unitary Systems
DOI:
https://doi.org/10.5281/zenodo.11531447Anahtar Kelimeler:
Phase retrieval, Norm retrieval, Frame vectors, Unitary systems Wandering subspacesÖzet
In a separable Hilbert space , we introduce phase and norm retrievable frame generators for a unitary system and show that phase retrievable and norm retrievable vectors and subspaces can be obtained with a unitary system structure. We give the conditions under which a complete wandering subspace for a unitary system can generate vectors and subspaces that do phase retrieval and norm retrieval in .
Referanslar
Dai, X., & Larson, D. R. (1998). Wandering vectors for unitary systems and orthogonal wavelets (Vol. 640). American Mathematical Soc..
Han, D. (1998). Wandering vectors for irrational rotation unitary systems. Transactions of the American Mathematical Society, 350(1), 309-320.
Robertson, J. B. (1965). On wandering subspaces for unitary operators. Proceedings of the American Mathematical Society, 16(2), 233-236.
Goodman, T. N. T., Lee, S. L., & Tang, W. S. (1993). Wavelets in wandering subspaces. Transactions of the American Mathematical Society, 338(2), 639-654.
Halmos, P. R. (1961). Shifts on Hilbert spaces.
Candès, E. J., & Donoho, D. L. (2004). New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 57(2), 219-266.
Daubechies, I. (1992). Ten lectures on wavelets. Society for industrial and applied mathematics.
Feichtinger, H. G., & Strohmer, T. (Eds.). (2012). Gabor analysis and algorithms: Theory and applications. Springer Science & Business Media.
Balan, R., Casazza, P., & Edidin, D. (2006). On signal reconstruction without phase. Applied and Computational Harmonic Analysis, 20(3), 345-356.
Bahmanpour, S., Cahill, J., Casazza, P. G., Jasper, J., & Woodland, L. M. (2014). Phase retrieval and norm retrieval. arXiv preprint arXiv:1409.8266.
Botelho-Andrade, S., Casazza, P. G., Van Nguyen, H., & Tremain, J. C. (2016). Phase retrieval versus phaseless reconstruction. Journal of Mathematical Analysis and Applications, 436(1), 131-137.
Casazza, P. G., Ghoreishi, D., Jose, S., & Tremain, J. C. (2017). Norm retrieval and phase retrieval by projections. Axioms, 6(1), 6.
Casazza, P. G., & Kutyniok, G. (2004). Frames of subspaces. Contemporary Mathematics, 345, 87-114.
Christensen, O. (2003). An introduction to frames and Riesz bases (Vol. 7). Boston: Birkhäuser.
Casazza, P. G., Kutyniok, G., & Philipp, F. (2013). Introduction to finite frame theory. Finite frames: theory and applications, 1-53.
Bhattacharjee, M., Eschmeier, J., Keshari, D. K., & Sarkar, J. (2017). Dilations, wandering subspaces, and inner functions. Linear Algebra and its Aapplications, 523, 263-280.
Liu, A., & Li, P. (2016). Wandering subspaces and fusion frame generators for unitary systems.
Han, D., Larson, D. R., Papadakis, M., & Stavropoulos, T. (1999). Multiresolution analyses of abstract Hilbert spaces and wandering subspaces. Contemporary Mathematics, 247, 259-284.
Duffin, R. J., & Schaeffer, A. C. (1952). A class of nonharmonic Fourier series. Transactions of the American Mathematical Society, 72(2), 341-366.
İndir
Yayınlanmış
Nasıl Atıf Yapılır
Sayı
Bölüm
Lisans
Telif Hakkı (c) 2024 Journal on Mathematic, Engineering and Natural Sciences (EJONS)
Bu çalışma Creative Commons Attribution-NonCommercial 4.0 International License ile lisanslanmıştır.