共查询到20条相似文献,搜索用时 109 毫秒
1.
2.
We obtain characterizations (and prove the corresponding equivalence of norms) of function spaces B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) of Nikol’skii-Besov and Lizorkin-Triebel types, respectively, in terms of representations of functions in these spaces by
Fourier series with respect to a multiple system $
\mathcal{W}_m^\mathbb{I}
$
\mathcal{W}_m^\mathbb{I}
of Meyer wavelets and in terms of sequences of the Fourier coefficients with respect to this system. We establish order-sharp
estimates for the approximation of functions in B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) by special partial sums of these series in the metric of L
r
($
\mathbb{I}
$
\mathbb{I}
k
) for a number of relations between the parameters s, p, q, r, and m (s = (s
1, ..., s
n
) ∈ ℝ+
n
, 1 ≤ p, q, r ≤ ∞, m = (m
1, ..., m
n
) ∈ ℕ
n
, k = m
1 +... + m
n
, and $
\mathbb{I}
$
\mathbb{I}
= ℝ or $
\mathbb{T}
$
\mathbb{T}
). In the periodic case, we study the Fourier widths of these function classes. 相似文献
3.
In this paper, we introduce the subfamilies H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) of holomorphic mappings defined on the Lie ball $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n) which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m = 1 and m → +∞, respectively. Various distortion theorems for holomophic mappings H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are established. The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk. When m = 1 and m → +∞, the distortion theorems reduce to the results obtained by Gong for $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are given. 相似文献
4.
E. A. Kudryavtseva 《Moscow University Mathematics Bulletin》2009,64(4):150-158
Let M be a smooth compact (orientable or not) surface with or without a boundary. Let $
\mathcal{D}_0
$
\mathcal{D}_0
⊂ Diff(M) be the group of diffeomorphisms homotopic to id
M
. Two smooth functions f, g: M → ℝ are called isotopic if f = h
2 ℴ g ℴ h
1 for some diffeomorphisms h
1 ∈ $
\mathcal{D}_0
$
\mathcal{D}_0
and h
2 ∈ Diff+(ℝ). Let F be the space of Morse functions on M which are constant on each boundary component and have no critical points on the boundary. A criterion for two Morse functions
from F to be isotopic is proved. For each Morse function f ∈ F, a collection of Morse local coordinates in disjoint circular neighborhoods of its critical points is constructed, which
continuously and Diff(M)-equivariantly depends on f in C
∞-topology on F (“uniform Morse lemma”). Applications of these results to the problem of describing the homotopy type of the space F are formulated. 相似文献
5.
Marilyn Breen 《Periodica Mathematica Hungarica》2009,59(1):99-107
Fix k, d, 1 ≤ k ≤ d + 1. Let $
\mathcal{F}
$
\mathcal{F}
be a nonempty, finite family of closed sets in ℝ
d
, and let L be a (d − k + 1)-dimensional flat in ℝ
d
. The following results hold for the set T ≡ ∪{F: F in $
\mathcal{F}
$
\mathcal{F}
}.
Assume that, for every k (not necessarily distinct) members F
1, …, F
k
of $
\mathcal{F}
$
\mathcal{F}
,∪{F
i
: 1 ≤ i ≤ k} is starshaped and the corresponding kernel contains a translate of L. Then T is starshaped, and its kernel also contains a translate of L. 相似文献
6.
Let M be a smooth manifold with a regular foliation $
\mathcal{F}
$
\mathcal{F}
and a 2-form ω which induces closed forms on the leaves of $
\mathcal{F}
$
\mathcal{F}
in the leaf topology. A smooth map f: (M, $
\mathcal{F}
$
\mathcal{F}
) → (N, σ) in a symplectic manifold (N, σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the restriction of f*σ is the same as the restriction of ω on each leaf of the foliation.
If f is a foliated symplectic immersion then the derivative map Df gives rise to a bundle morphism F: TM → T N which restricts to a monomorphism on T
$
\mathcal{F}
$
\mathcal{F}
⊆ T M and satisfies the condition F*σ = ω on T
$
\mathcal{F}
$
\mathcal{F}
. A natural question is whether the existence of such a bundle map F ensures the existence of a foliated symplectic immersion f. As we shall see in this paper, the obstruction to the existence of such an f is only topological in nature. The result is proved using the h-principle theory of Gromov. 相似文献
7.
Spiros A. Argyros Irene Deliyanni Andreas G. Tolias 《Israel Journal of Mathematics》2011,181(1):65-110
We provide a characterization of the Banach spaces X with a Schauder basis (e
n
)
n∈ℕ which have the property that the dual space X* is naturally isomorphic to the space L
diag(X) of diagonal operators with respect to (e
n
)
n∈ℕ. We also construct a Hereditarily Indecomposable Banach space $
\mathfrak{X}
$
\mathfrak{X}
D with a Schauder basis (e
n
)
n∈ℕ such that $
\mathfrak{X}
$
\mathfrak{X}
*D is isometric to L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every T ∈ L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) is of the form T = λI + K, where K is a compact operator. 相似文献
8.
Heinrich P. Lotz 《Israel Journal of Mathematics》2010,176(1):209-220
We consider a Dedekind σ-complete Banach lattice E whose dual is weakly sequentially complete. Suppose that E has a positive element u and a family of positive operators $
\mathcal{G}
$
\mathcal{G}
such that
(i) |
each T′, T ∈ $
\mathcal{G}
$
\mathcal{G}
, is a lattice homomorphism 相似文献
9.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
10.
S. A. Nazarov 《Journal of Applied and Industrial Mathematics》2009,3(3):377-390
Taking various viewpoints, we study the selfadjoint extensions $
\mathcal{A}
$
\mathcal{A}
of the operator A of the Dirichlet problem in a 3-dimensional region Ω with an edge Γ. We identify the infinite dimensional nullspace def A with the Sobolev space H
−ϰ(Γ) on Γ with variable smoothness exponent −ϰ ∈ (−1, 0); while the selfadjoint extensions, with selfadjoint operators $
\mathcal{T}
$
\mathcal{T}
on the subspaces of H
−ϰ(Γ). To the boundary value problem in the region with a “smoothed” edge we associate a concrete extension, which yields a
more precise approximate solution to the singularly perturbed problem. 相似文献
11.
F. Chebana 《Mathematical Methods of Statistics》2009,18(3):231-240
Consider a class of M-estimators indexed by a criterion function ψ. When the function ψ is taken to be in a class of functions $
\mathcal{F}
$
\mathcal{F}
, a family of processes indexed by the class $
\mathcal{F}
$
\mathcal{F}
is obtained and called M-processes. Pooling the M-estimators in such class may be used to define new kind of estimators. In order to get the asymptotic properties of these
pooled estimators, the convergence in probability of the corresponding M-process is studied uniformly on $
\mathcal{F}
$
\mathcal{F}
together with their weak convergence towards a Gaussian process. An application to location estimation is presented and discussed. 相似文献
12.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
|