Results 241 to 250 of about 525,025 (272)
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Advances in Computational Mathematics, 2003
We study the set of tight frame wavelets, and characterize its various important subsets. For example, we prove that a TFW is an MRA TFW if and only if its dimension function is either zero or one. We also prove that the set of MSF TFW-s is connected.
Paluszyński, Maciej +3 more
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We study the set of tight frame wavelets, and characterize its various important subsets. For example, we prove that a TFW is an MRA TFW if and only if its dimension function is either zero or one. We also prove that the set of MSF TFW-s is connected.
Paluszyński, Maciej +3 more
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On p-adic tight wavelet frames
Journal of Mathematical Analysis and Applications, 2023The authors design tight wavelet frames on the field of \(p\)-adic numbers. To this purpose, Pontryagin's principle of duality on zero-dimensional groups is exploited instead of the unitary extension principle. The most of results are formulated for an arbitrary zero-dimensional group with a mild technical restriction.
Lukomskii, S. F., Vodolazov, A. M.
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Expansion of frames to tight frames
Acta Mathematica Sinica, English Series, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Dengfeng, Sun, Wenchang
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Doklady Mathematics, 2008
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Vestnik St. Petersburg University: Mathematics, 2009
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Equal-Norm Tight Frames with Erasures
Advances in Computational Mathematics, 2003Given a Hilbert space \(H\), a collection \(\{e_i: i \in I \} \subset H\) is called a frame if there exist constants \(A, B>0\) such that for all \(f\in H\): \[ A \| f\| ^2 \leq \sum_{i \in I} | \langle f, e_i \rangle | ^2 \leq B \| f\| ^2. \] When \(A=B\) we say that the frame is tight. When all elements \(e_i\) have the same norm, we say the frame is
Casazza, Peter G., Kovačević, Jelena
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Construction of Tight Filter Bank Frames
2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006In this paper, we present an explicit and numerically efficient formulae to construct a tight (paraunitary) FB frame from a given un-tight (non-paraunitary) FB frame. The derivation uses the well developed techniques from modern control theory, which results in the unified formulae for generic IIR and FIR FBs.
Chai, Li +3 more
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Complex equiangular tight frames
SPIE Proceedings, 2005A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in C d whose absolute inner products are identical. One may view complex ETFs as a natural geometric generalization of an orthonormal basis. Numerical evidence suggests that these objects do not arise for most pairs ( d , N).
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Tight Frames and Dual Frame Pairs
2016We have already highlighted the frame decomposition, which shows that a frame \(\{f_{k}\}_{k=1}^{\infty }\) for a Hilbert space \(\mathcal{H}\) leads to the decomposition $$\displaystyle\begin{array}{rcl} f =\sum _{ k=1}^{\infty }\langle f,S^{-1}f_{ k}\rangle f_{k},\ \ \forall f \in \mathcal{H};& &{}\end{array}$$ (6.1) here \(S: \mathcal{H ...
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2018
The angle preserving transformations of \(\mathbb {R}^2\) form the real orthogonal group $${ O}(2) := \{A\in \mathbb {R}^{2\times 2}:A^T A=I\},$$ which can be thought of as the symmetries of the inner product space \({\mathscr {H}}=\mathbb {R}^2\).
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The angle preserving transformations of \(\mathbb {R}^2\) form the real orthogonal group $${ O}(2) := \{A\in \mathbb {R}^{2\times 2}:A^T A=I\},$$ which can be thought of as the symmetries of the inner product space \({\mathscr {H}}=\mathbb {R}^2\).
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