共查询到20条相似文献,搜索用时 281 毫秒
1.
Let j{\varphi} be an analytic self-map of the unit disk
\mathbbD{\mathbb{D}},
H(\mathbbD){H(\mathbb{D})} the space of analytic functions on
\mathbbD{\mathbb{D}} and
g ? H(\mathbbD){g \in H(\mathbb{D})}. The boundedness and compactness of the operator DCj : H¥ ? Z{DC_\varphi : H^\infty \rightarrow { \mathcal Z}} are investigated in this paper. 相似文献
2.
We propose an algorithm to sample and mesh a k-submanifold M{\mathcal{M}} of positive reach embedded in
\mathbbRd{\mathbb{R}^{d}} . The algorithm first constructs a crude sample of M{\mathcal{M}} . It then refines the sample according to a prescribed parameter e{\varepsilon} , and builds a mesh that approximates M{\mathcal{M}} . Differently from most algorithms that have been developed for meshing surfaces of
\mathbbR 3{\mathbb{R} ^3} , the refinement phase does not rely on a subdivision of
\mathbbR d{\mathbb{R} ^d} (such as a grid or a triangulation of the sample points) since the size of such scaffoldings depends exponentially on the
ambient dimension d. Instead, we only compute local stars consisting of k-dimensional simplices around each sample point. By refining the sample, we can ensure that all stars become coherent leading
to a k-dimensional triangulated manifold [^(M)]{\hat{\mathcal{M}}} . The algorithm uses only simple numerical operations. We show that the size of the sample is O(e-k){O(\varepsilon ^{-k})} and that [^(M)]{\hat{\mathcal{M}}} is a good triangulation of M{\mathcal{M}} . More specifically, we show that M{\mathcal{M}} and [^(M)]{\hat{\mathcal{M}}} are isotopic, that their Hausdorff distance is O(e2){O(\varepsilon ^{2})} and that the maximum angle between their tangent bundles is O(e){O(\varepsilon )} . The asymptotic complexity of the algorithm is T(e) = O(e-k2-k){T(\varepsilon) = O(\varepsilon ^{-k^2-k})} (for fixed M, d{\mathcal{M}, d} and k). 相似文献
3.
4.
Clément de Seguins Pazzis 《Archiv der Mathematik》2010,95(4):333-342
When
\mathbbK{\mathbb{K}} is an arbitrary field, we study the affine automorphisms of
Mn(\mathbbK){{\rm M}_n(\mathbb{K})} that stabilize
GLn(\mathbbK){{\rm GL}_n(\mathbb{K})}. Using a theorem of Dieudonné on maximal affine subspaces of singular matrices, this is easily reduced to the known case
of linear preservers when n > 2 or # ${\mathbb{K} > 2}${\mathbb{K} > 2}. We include a short new proof of the more general Flanders theorem for affine subspaces of
Mp,q(\mathbbK){{\rm M}_{p,q}(\mathbb{K})} with bounded rank. We also find that the group of affine transformations of
M2(\mathbbF2){{\rm M}_2(\mathbb{F}_2)} that stabilize
GL2(\mathbbF2){{\rm GL}_2(\mathbb{F}_2)} does not consist solely of linear maps. Using the theory of quadratic forms over
\mathbbF2{\mathbb{F}_2}, we construct explicit isomorphisms between it, the symplectic group
Sp4(\mathbbF2){{\rm Sp}_4(\mathbb{F}_2)} and the symmetric group
\mathfrakS6{\mathfrak{S}_6}. 相似文献
5.
Matteo Dalla Riva Massimo Lanza de Cristoforis 《Complex Analysis and Operator Theory》2011,5(3):811-833
Let Ω
i
and Ω
o
be two bounded open subsets of
\mathbbRn{{\mathbb{R}}^{n}} containing 0. Let G
i
be a (nonlinear) map from
?Wi×\mathbbRn{\partial\Omega^{i}\times {\mathbb{R}}^{n}} to
\mathbbRn{{\mathbb{R}}^{n}} . Let a
o
be a map from ∂Ω
o
to the set
Mn(\mathbbR){M_{n}({\mathbb{R}})} of n × n matrices with real entries. Let g be a function from ∂Ω
o
to
\mathbbRn{{\mathbb{R}}^{n}} . Let γ be a positive valued function defined on a right neighborhood of 0 in the real line. Let T be a map from
]1-(2/n),+¥[×Mn(\mathbbR){]1-(2/n),+\infty[\times M_{n}({\mathbb{R}})} to
Mn(\mathbbR){M_{n}({\mathbb{R}})} . Then we consider the problem
$\left\{ {ll} {{\rm div}}\, (T(\omega,Du))=0 &\quad {{\rm in}} \;\Omega^{o} \setminus\epsilon{{\rm cl}} \Omega^{i},\\ -T(\omega,Du(x))\nu_{\epsilon\Omega^{i}}(x)=\frac{1}{\gamma(\epsilon)}G^{i}({x}/{\epsilon}, \gamma(\epsilon)\epsilon^{-1} ({\rm log} \, \epsilon)^{-\delta_{2,n}} u(x)) & \quad \forall x \in \epsilon\partial\Omega^{i},\\ T(\omega, Du(x)) \nu^{o}(x)=a^{o}(x)u(x)+g(x) & \quad \forall x \in \partial \Omega^{o}, \right.$\left\{ \begin{array}{ll} {{\rm div}}\, (T(\omega,Du))=0 &\quad {{\rm in}} \;\Omega^{o} \setminus\epsilon{{\rm cl}} \Omega^{i},\\ -T(\omega,Du(x))\nu_{\epsilon\Omega^{i}}(x)=\frac{1}{\gamma(\epsilon)}G^{i}({x}/{\epsilon}, \gamma(\epsilon)\epsilon^{-1} ({\rm log} \, \epsilon)^{-\delta_{2,n}} u(x)) & \quad \forall x \in \epsilon\partial\Omega^{i},\\ T(\omega, Du(x)) \nu^{o}(x)=a^{o}(x)u(x)+g(x) & \quad \forall x \in \partial \Omega^{o}, \end{array} \right. 相似文献
6.
Let X be a realcompact space and H:C(X)?\mathbbR{H:C(X)\rightarrow\mathbb{R}} be an identity and order preserving group homomorphism. It is shown that H is an evaluation at some point of X if and only if there is j ? C(\mathbbR){\varphi\in C(\mathbb{R})} with ${\varphi(r)>\varphi(0)}${\varphi(r)>\varphi(0)} for all r ? \mathbbR-{0}{r\in\mathbb{R}-\{0\}} for which H°j = j°H{H\circ\varphi=\varphi\circ H} . This extends (and unifies) classical results by Hewitt and Shirota. 相似文献
7.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}
8.
We characterize when an ideal of the algebra ${A(\mathbb{R}^d)}
9.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}
10.
Nikolaos Bournaveas Timothy Candy 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(1):67-78
It is known from Czubak (Anal PDE 3(2):151–174, 2010) that the space–time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} for ${s>\frac{1}{4}}${s>\frac{1}{4}}. Here we prove local well-posedness for arbitrary initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} with ${s>\frac{1}{4}}${s>\frac{1}{4}} in the Lorenz gauge. 相似文献
11.
Cauchy’s problem for a generalization of the KdV–Burgers equation is considered in Sobolev spaces
H1(\mathbbR){H^1(\mathbb{R})} and
H2(\mathbbR){H^2(\mathbb{R})}. We study its local and global solvability and the asymptotic behavior of solutions (in terms of the global attractors).
The parabolic regularization technique is used in this paper which allows us to extend the strong regularity properties and
estimates of solutions of the fourth order parabolic approximations onto their third order limit—the generalized Korteweg–de
Vries–Burgers (KdVB) equation. For initial data in
H2(\mathbbR){H^2(\mathbb{R})} we study the notion of viscosity solutions to KdVB, while for the larger
H1(\mathbbR){H^1(\mathbb{R})} phase space we introduce weak solutions to that problem. Finally, thanks to our general assumptions on the nonlinear term f guaranteeing that the global attractor is usually nontrivial (i.e., not reduced to a single stationary solution), we study
an upper semicontinuity property of the family of global attractors corresponding to parabolic regularizations when the regularization
parameter e{\epsilon} tends to 0+ (which corresponds the passage to the KdVB equation). 相似文献
12.
Laura Paladino 《Annali di Matematica Pura ed Applicata》2010,189(1):17-23
Let ${\mathcal{E}}
13.
Let ${\mathbb {F}}
14.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
15.
David Fried 《Journal of Fixed Point Theory and Applications》2009,6(1):87-92
When X is a finite complex and p1X\pi_{1}X acts on
\mathbbR2{\mathbb{R}}^2 by translations we give criteria involving H2X for an equivariant map
F : [(X)\tilde] ? \mathbbR2F : \tilde{X} \rightarrow {\mathbb{R}}^2 to be onto. Following work of Manning and Shub, this leads to entropy bounds related to Shub’s entropy conjecture. 相似文献
16.
We show that if A is a closed analytic subset of
\mathbbPn{\mathbb{P}^n} of pure codimension q then
Hi(\mathbbPn\ A,F){H^i(\mathbb{P}^n{\setminus} A,{\mathcal F})} are finite dimensional for every coherent algebraic sheaf F{{\mathcal F}} and every
i 3 n-[\fracn-1q]{i\geq n-\left[\frac{n-1}{q}\right]} . If
n-1 3 2q we show that Hn-2(\mathbbPn\ A,F)=0{n-1\geq 2q\,{\rm we show that}\, H^{n-2}(\mathbb{P}^n{\setminus} A,{\mathcal F})=0} . 相似文献
17.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
18.
A variety ${\mathbb{V}}${\mathbb{V}} is var-relatively universal if it contains a subvariety
\mathbbW{\mathbb{W}} such that the class of all homomorphisms that do not factorize through any algebra in
\mathbbW{\mathbb{W}} is algebraically universal. And
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} if adding α nullary operations to all algebras in
\mathbbV{\mathbb{V}} gives rise to a class
a\mathbbV{\alpha\mathbb{V}} of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} . This note contains a more general result that proves this conjecture. 相似文献
19.
20.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献
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