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Letter to the Editor: Linear Independence of Time-Frequency Shifts Up To Extreme Dilations
Springer Science and Business Media LLC - Tập 25 - Trang 3214-3219 - 2019
Michael Kreisel
Given $$f \in C_0({{\,\mathrm{\mathbb {R}}\,}}^n)$$ and a finite set $$\Lambda \subset {{\,\mathrm{\mathbb {R}}\,}}^{2n}$$ we demonstrate the linear independence of the set of time-frequency translates $$\mathcal {G}(f, \Lambda ) = \{\pi (\lambda )f\}_{\lambda \in \Lambda }$$ when the time coordinates of points in $$\Lambda $$ are far apart relative to the decay of f. As a corollary, we prove that... hiện toàn bộ
Tính khả giải L p của bài toán Dirichlet cho các phương trình elliptic trong mặt phẳng, Các kết quả chính xác Dịch bởi AI
Springer Science and Business Media LLC - Tập 15 - Trang 871-903 - 2009
Carlo Sbordone, Gabriella Zecca
Giả sử rằng toán tử elliptic L=div (A(x)∇) là L p -khả giải, p>1, trên đĩa đơn vị $\mathbb{D}\subset \mathbb {R}^{2}$ . Điều này có nghĩa là bài toán Dirichlet $$\left\{\begin{array}{l@{\quad}l}Lu=0&\mbox{trong }\mathbb{D},\\[3pt]u=g&\mbox{trên }\partial\mathbb{D}\end{array}\right.$$ có nghiệm duy nhất cho bất kỳ $g\in L^{p}(\partial\mathbb{D})$ . Sau đó, tồn tại ε>0 sao cho L là L r - khả giải tr... hiện toàn bộ
Bochner–Riesz Means of Morrey Functions
Springer Science and Business Media LLC - Tập 26 - Trang 1-14 - 2020
David R. Adams, Jie Xiao
This paper concerns both norm estimation and pointwise approximation for the Bochner–Riesz means of an arbitrary Morrey function on $${{{{\mathbb {R}}}}^n}$$—Theorems 1.1 and 1.2 for $$L^{p,\lambda }({{{{\mathbb {R}}}}^n})$$—thereby generalizing the corresponding results for $$L^p({{{{\mathbb {R}}}}^n})$$ in Stein (Acta Math 100:93–147, 1958) and Carbery et al. (J Lond Math Soc 38:513–524, 1988). ... hiện toàn bộ
Characterization of biorthogonal cosine wavelets
Springer Science and Business Media LLC - - 1997
Charles K. Chui, Xianliang Shi
This paper is devoted to the study of characterization of two-overlapping dual window functions that give rise to biorthogonal Schauder bases, frames, and Riesz bases by modulation of the cosines. We show that in this case any frame is a Riesz basis and our characterization of Riesz bases may be considered as a generalization of the theorems established by Coifman, et al. [6] and by Jawerth and Sw... hiện toàn bộ
An Analogue of Slepian Vectors on Boolean Hypercubes
Springer Science and Business Media LLC - Tập 25 - Trang 2004-2020 - 2018
Jeffrey A. Hogan, Joseph D. Lakey
Analogues of Slepian vectors are defined for finite-dimensional Boolean hypercubes. These vectors are the most concentrated in neighborhoods of the origin among bandlimited vectors. Spaces of bandlimited vectors are defined as spans of eigenvectors of the Laplacian of the hypercube graph with lowest eigenvalues. A difference operator that almost commutes with space and band limiting is used to ini... hiện toàn bộ
Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise
Springer Science and Business Media LLC - Tập 28 Số 2 - Trang 1-38 - 2022
Lee, Cheuk Yin
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong local nondeterminism of the solution and the existence of jointly continuous local times. We also study the differentiability and moduli of conti... hiện toàn bộ
The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces
Springer Science and Business Media LLC - Tập 4 - Trang 175-197 - 1998
Boris Rubin
The generalized Calderón reproducing formula involving “wavelet measure” is established for functions f ∈ Lp(ℝn). The special choice of the wavelet measure in the reproducing formula gives rise to the continuous decomposition of f into wavelets, and enables one to obtain inversion formulae for generalized windowed X-ray transforms, the Radon transform, and k-plane transforms. The admissibility con... hiện toàn bộ
On the stability of wavelet and Gabor frames (Riesz bases)
Springer Science and Business Media LLC - Tập 5 - Trang 105-125 - 1999
Zhang Jing
If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at... hiện toàn bộ
On boundary behavior of harmonic functions in Hölder domains
Springer Science and Business Media LLC - - 1998
Fausto Ferrari
Letter to the Editor: Stockwell and Wavelet Transforms
Springer Science and Business Media LLC - Tập 12 - Trang 713-721 - 2006
Peter C. Gibson, Michael P. Lamoureux, Gary F. Margrave
Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis. It is the purpose of this letter to encourage the interaction between the wavelet and the Stockwell communities by demonstrating that—up to minor modifications—the S-transform is a special case of the well-known continuous wavelet transform via a Morlet-type mother wavelet, with... hiện toàn bộ
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