Results 11 to 20 of about 42 (42)
Journal of Function Spaces, Volume 6, Issue 2, Page 107-154, 2008., 2008 A construction of Triebel‐Lizorkin type spaces associated with flexible decompositions of the frequency space ℝd is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on ℝd and a suitable decomposition function.
Lasse Borup +2 more
wiley +1 more source
Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 6, Page 285-293, 2004., 2004 We define and study Dunkl wavelets and the corresponding Dunkl wavelets transforms, and we prove for these transforms Plancherel and reconstruction formulas. We give as application the inversion of the Dunkl intertwining operator and its dual.
Abdellatif Jouini
wiley +1 more source
Vanishing moments for scaling vectors
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 36, Page 1897-1908, 2004., 2004 One advantage of scaling vectors over a single scaling function is the compatibility of symmetry and orthogonality. This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vector Φ. Some general results on scaling vectors and vanishing moments are developed, as well as some necessary
David K. Ruch
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Infinite matrices, wavelet coefficients and frames
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 67, Page 3695-3702, 2004., 2004 We study the action of A on f ∈ L2(ℝ) and on its wavelet coefficients, where A=(almjk) lmjk is a double infinite matrix. We find the frame condition for A‐transform of f ∈ L2(ℝ) whose wavelet series expansion is known.
N. A. Sheikh, M. Mursaleen
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Reconstruction in time‐warped weighted shift‐invariant spaces with application to spline subspaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 65, Page 4131-4137, 2003., 2003 We discuss the reproducing kernel structure in shift‐invariant spaces and the weighted shift‐invariant spaces, and obtain the reconstruction formula in time‐warped weighted shift‐invariant spaces, then apply them to a spline subspace. In the spline subspace, we give a reconstruction formula in a time‐warped spline subspace.
Jun Xian, Yongjin Li
wiley +1 more source
Hardy‐Littlewood type inequalities for Laguerre series
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 9, Page 533-540, 2002., 2002 Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr‐convergence of Laguerre series ∑cj𝔏ja. Then, we prove a Hardy‐Littlewood type inequality ∫0∞|f(t)|rdt≤C∑j=0∞|cj|rj¯12−r/ for certain r ≤ 1, where f is the limit function of ∑cj𝔏ja.
Chin-Cheng Lin, Shu-Huey Lin
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Biorthogonal multiresolution analyses and decompositions of Sobolev spaces
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 9, Page 517-534, 2001., 2001 The object of this paper is to construct extension operators in the Sobolev spaces Hk(]−∞, 0]) and Hk([0, +∞[)(k ≥ 0). Then we use these extensions to get biorthogonal wavelet bases in Hk(ℝ). We also give a construction in L2([−1, 1]) to see how to obtain boundaries functions.
Abdellatif Jouini, Khalifa Trimèche
wiley +1 more source
Characterization and Construction of Phase Retrievable Sequences
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, we study phase retrievable sequences and give a characterization of phase retrievability of a sequence of bounded linear operators on a Hilbert space H; in particular, for H=l2dℂ. We also give several approaches for constructing phase retrievable sequences. Then, we investigate the property of phase retrievable for g‐frames and frames.
F. Javadi +2 more
wiley +1 more source
Sampling Trajectories for the Short-Time Fourier Transform. [PDF]
J Fourier Anal Appl, 2022 Speckbacher M.
europepmc +1 more source
Localization of Fréchet Frames and Expansion of Generalized Functions. [PDF]
Bull Malays Math Sci Soc, 2021 Pilipović S, Stoeva DT.
europepmc +1 more source