| Autor: |
Tufail Hussain, Yun-Zhang Li |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-14 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
1029-242X |
| DOI: |
10.1186/s13660-020-02331-x |
| Popis: |
Abstract Structured frames such as wavelet and Gabor frames in L 2 ( R ) $L^{2}(\mathbb {R})$ have been extensively studied. But L 2 ( R + ) $L^{2}(\mathbb{ R}_{+})$ cannot admit wavelet and Gabor systems due to R + $\mathbb{R}_{+}$ being not a group under addition. In practice, L 2 ( R + ) $L^{2}(\mathbb{R}_{+})$ models the causal signal space. The function-valued inner product-based F a $F_{a}$ -frame for L 2 ( R + ) $L^{2}(\mathbb{R}_{+})$ was first introduced by Hasankhani Fard and Dehghan, where an F a $F_{a}$ -frame was called a function-valued frame. In this paper, we introduce the notions of F a $F_{a}$ -equivalence and unitary F a $F_{a}$ -equivalence between F a $F_{a}$ -frames, and present a characterization of the F a $F_{a}$ -equivalence and unitary F a $F_{a}$ -equivalence. This characterization looks like that of equivalence and unitary equivalence between frames, but the proof is nontrivial due to the particularity of F a $F_{a}$ -frames. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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