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1.
Parseval Frame Wavelet Multipliers in L2(Rd) 总被引:1,自引:0,他引:1
Let A be a d × d real expansive matrix. An A-dilation Parseval frame wavelet is a function ?? ?? L 2(? d ), such that the set $ \left\{ {\left| {\det A} \right|^{\frac{n} {2}} \psi \left( {A^n t - \ell } \right):n \in \mathbb{Z},\ell \in \mathbb{Z}^d } \right\} $ forms a Parseval frame for L 2(? d ). A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of d??? is an A-dilation Parseval frame wavelet whenever ?? is an A-dilation Parseval frame wavelet, where ??? denotes the Fourier transform of ??. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with |det(A)| = 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L 2(? d ) is discussed. 相似文献
2.
Lars Olsen 《Aequationes Mathematicae》2013,86(1-2):23-56
In this paper we study the Hausdorff and packing dimensions and the Rényi dimensions of random self-affine multifractal Sierpinski sponges in ${{\mathbb{R}}^{d}}$ . 相似文献
3.
Marilyn Breen 《Aequationes Mathematicae》2014,87(1-2):43-52
Let S be an orthogonal polytope in ${\mathbb{R}^d}$ . There exists a suitable family ${\mathcal{C}}$ of boxes with ${S = \cup \{C : C {\rm in} \mathcal{C}\}}$ such that the following properties hold: The staircase kernel Ker S is a union of boxes in ${\mathcal{C}}$ . Let ${\mathcal{V}}$ be the family of vertices of boxes in ${\mathcal{C}}$ , and let ${v_o\, \epsilon \mathcal{V}}$ . Point v o belongs to Ker S if and only if v o sees via staircase paths in S every point w in ${\mathcal{V}}$ . Moreover, these staircase paths may be selected to consist of edges of boxes in ${\mathcal{C}}$ . Let B be a box in ${\mathcal{C}}$ with vertices of B in Ker S. Box B lies in Ker S if and only if, for some b in rel int B and for every translate H of a coordinate hyperplane at ${b, b \epsilon}$ Ker (H ∩ S). For point p in S, p belongs to Ker S if and only if, for every x in S, there exist some p ? x geodesic λ (p, x) and some corresponding ${\mathcal{C}}$ - chain D containing λ (p, x) such that D is staircase starshaped at p. 相似文献
4.
For one of Thurston model spaces, \({\widetilde{{\rm SL}_2({\mathbb{R}})}}\) , we discuss translation balls and packing that space by such balls in contrast to the packing by standard (geodesic) balls. We present an infinite family of packings generated by discrete groups of isometries, and observe numerical results on their densities. In particular, we found packings whose densities are close to the upper bound density for ball packings in the hyperbolic 3-space. 相似文献
5.
6.
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier series. Equivalent conditions
are derived for the uniform and L
1-norm convergence of the θ-means σ
n
θ
f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case θ is an element
of Feichtinger’s Segal algebra
, then these convergence results hold. Some new sufficient conditions are given for θ to be in
. A long list of concrete special cases of the θ-summation is listed. The same results are also provided in the context of
Fourier transforms, indicating how proofs have to be changed in this case.
This research was supported by Lise Meitner fellowship No M733-N04 and the Hungarian Scientific Research Funds (OTKA) No T043769,
T047128, T047132. 相似文献
7.
Najmeddine Attia 《Journal of Theoretical Probability》2014,27(4):1329-1349
We establish the almost sure validity of the multifractal formalism for \(\mathbb{R }^d\) -valued branching random walks on the whole relative interior of the natural convex domain of study. 相似文献
8.
Joseph Zaks 《Journal of Geometry》2005,82(1-2):195-203
Benz proved that every mapping
that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping
that preserves the distances 1 and
is an isometry, provided d ≥ 5. 相似文献
9.
Jingwei Guo 《Archiv der Mathematik》2017,108(1):45-53
We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy. 相似文献
10.
We consider an algebra of operator sequences containing, among others, the approximation sequences to convolution type operators
on cones acting on
Lp(\mathbb R2)L^{p}(\mathbb {R}^2), with 1 < p < ∞. To each operator sequence (An) we associate a family of operators
Wx(An) ? L(Lp(\mathbb R2))W_{x}(A_{n}) \in \mathcal {L}(L^{p}(\mathbb {R}^2)) parametrized by x in some index set. When all Wx(An) are Fredholm, the so-called approximation numbers of An have the α-splitting property with α being the sum of the kernel dimensions of Wx(An). Moreover, the sum of the indices of Wx(An) is zero. We also show that the index of some composed convolution-like operators is zero. Results on the convergence of
the e\epsilon-pseudospectrum, norms of inverses and condition numbers are also obtained. 相似文献
11.
We consider the standard first passage percolation model in the rescaled graph ${\mathbb{Z}^d/n}$ for d??? 2, and a domain ?? of boundary ?? in ${\mathbb{R}^d}$ . Let ??1 and ??2 be two disjoint open subsets of ??, representing the parts of ?? through which some water can enter and escape from ??. We investigate the asymptotic behaviour of the flow ${\phi_n}$ through a discrete version ?? n of ?? between the corresponding discrete sets ${\Gamma^{1}_{n}}$ and ${\Gamma^{2}_{n}}$ . We prove that under some conditions on the regularity of the domain and on the law of the capacity of the edges, the lower large deviations of ${\phi_n/ n^{d-1}}$ below a certain constant are of surface order. 相似文献
12.
13.
Let f_n be a non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in mathbb{R}^d. In this paper we prove two moderate deviation theorems in L_1(mathbb{R}^d) for {f_n(x)-f_n(-x),,nge1}. 相似文献
14.
Gioconda Moscariello Carlo Sbordone 《Journal of Fixed Point Theory and Applications》2007,1(2):337-350
Let
be a sequence of Borel measurable functions satisfying, for a function
the inequalities
and suppose
Then there exists a sequence of increasing homeomorphisms
converging to a homeomorphism
weakly in
and locally uniformly, such that
Dedicated to the memory of Jean Leray 相似文献
15.
R. Cavazzoni 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):193-204
In this paper we present a parabolic approach to studying the diffusive long time behaviour of solutions to the Cauchy problem:
where u0 and u1 satisfy suitable assumptions.
After an appropriate scaling we obtain the convergence to a stationary solutio n in Lq norm (1 ≤ q < ∞). 相似文献
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16.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right.$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right. 相似文献
17.
Given a Lie group G with a bi-invariant metric and a compact Lie subgroup K, Bittencourt and Ripoll used the homogeneous structure of quotient spaces to define a Gauss map ${\mathcal{N}:M^{n}\rightarrow{\mathbb{S}}}$ on any hypersupersurface ${M^{n}\looparrowright G/K}$ , where ${{\mathbb{S}}}$ is the unit sphere of the Lie algebra of G. It is proved in Bittencourt and Ripoll (Pacific J Math 224:45–64, 2006) that M n having constant mean curvature (CMC) is equivalent to ${\mathcal{N}}$ being harmonic, a generalization of a Ruh–Vilms theorem for submanifolds in the Euclidean space. In particular, when n = 2, the induced quadratic differential ${\mathcal{Q}_{\mathcal{N}}:=(\mathcal{N}^{\ast}g)^{2,0}}$ is holomorphic on CMC surfaces of G/K. In this paper, we take ${G/K={\mathbb{S}}^{2}\times{\mathbb{R}}}$ and compare ${\mathcal{Q}_{\mathcal{N}}}$ with the Abresch–Rosenberg differential ${\mathcal{Q}}$ , also holomorphic for CMC surfaces. It is proved that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ , after showing that ${\mathcal{N}}$ is the twisted normal given by (1.5) herein. Then we define the twisted normal for surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ and prove that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ as well. Within the unified model for the two product spaces, we compute the tension field of ${\mathcal{N}}$ and extend to surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ the equivalence between the CMC property and the harmonicity of ${\mathcal{N}.}$ 相似文献
18.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}
19.
We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries. 相似文献 |