آمار
| تعداد نشریات | 45 |
| تعداد شمارهها | 1,560 |
| تعداد مقالات | 19,038 |
| تعداد مشاهده مقاله | 64,651,058 |
| تعداد دریافت فایل اصل مقاله | 23,798,737 |
PHASE RETRIEVABILITY: FUSION FRAMES, RANK CHARACTERIZATIONS, DIMENSION FUNCTIONS, AND OPENNESS OF DUAL FRAMES | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آبان 1405 اصل مقاله (1001.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.72841.3690 | ||
| نویسندگان | ||
| Masoumeh Allahgholizadeh؛ Mohammad Hossein Sattari* | ||
| Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. | ||
| چکیده | ||
| This paper develops a unified algebraic framework for phase retrieval by subspaces and fusion frames in finite-dimensional Hilbert spaces. The classical complement property, known to be both necessary and sufficient for vector phase retrieval, is shown to be insufficient when extended to collections of subspaces. To address this limitation, the authors introduce a fusion frame dimension function and establish a precise rank characterization, proving that its value coincides with the rank of an associated linear operator. This structural result leads to several consequences: the openness of the set of phase retrievable dual frames, a continuity criterion equivalent to phase retrievability. The presented framework clarifies the interplay among the complement property and operator-theoretic rank conditions, thereby extending the foundational theory of phase retrieval beyond the vector case to a broader class of subspace and fusion frame systems. | ||
| کلیدواژهها | ||
| phase retrieval؛ frames؛ fusion frame؛ frame dimension function | ||
|
آمار تعداد مشاهده مقاله: 1 |
||