共查询到20条相似文献,搜索用时 31 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.
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M there exists a map g′: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $
\mathbb{I}
$
\mathbb{I}
n
) ≤ n for all z ∈ $
\mathbb{I}
$
\mathbb{I}
m
. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij
[11] and Tuncali-Valov [10]. 相似文献
4.
I. E. Zuber 《Vestnik St. Petersburg University: Mathematics》2010,43(3):139-142
A control of an nth-order discrete system under an external perturbation is considered. The elements of the matrix of the system are functionals
of any nature. The observation matrix is constant and has arbitrary size m × n. A control ensuring the independence of the output σ
k
on the external perturbation ψ
k
is synthesized; moreover,
$
\sigma _{k + 1} = \beta \sigma _k , 0 < \beta < 1, \sigma _k \in \mathbb{R}^m
$
\sigma _{k + 1} = \beta \sigma _k , 0 < \beta < 1, \sigma _k \in \mathbb{R}^m
相似文献
5.
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
6.
M. V. Deikalova 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):129-142
The best constant C
n,m
in the Jackson-Nikol’skii inequality between the uniform and integral norms of algebraic polynomials of a given total degree
n ≥ 0 on the unit sphere $
\mathbb{S}^{m - 1}
$
\mathbb{S}^{m - 1}
of the Euclidean space ℝ
m
is studied. Two-sided estimates for the constant C
n,m
are obtained, which, in particular, give the order n
m−1 of its behavior with respect to n as n → +∞ for a fixed m. 相似文献
7.
In this article we extend the notion of constant angle surfaces in $
\mathbb{S}^2
$
\mathbb{S}^2
× ℝ and ℍ2 × ℝ to general Bianchi-Cartan-Vranceanu spaces. We show that these surfaces have constant Gaussian curvature and we give
a complete local classification in the Heisenberg group. 相似文献
8.
In this note we construct a function φ in L2(Bn,dμ) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2(Bn,dμ) for several complex variables. 相似文献
9.
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space ℝ1+n
to the unit sphere $
\mathbb{S}
$
\mathbb{S}
2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms,
quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small
initial data in Sobolev space. 相似文献
10.
Ganesh C. Gorain 《Proceedings Mathematical Sciences》2010,120(4):495-506
We study the stabilization of vibrations of a flexible structure modeled by the ‘standard linear model’ of viscoelasticity
in a bounded domain in ℝ
n
with a smooth boundary. We prove that amplitude of the vibrations remains bounded in the sense of a suitable norm in a space
$
\mathbb{X}
$
\mathbb{X}
, defined explicitly in (22) subject to a restriction on the uncertain disturbing forces on $
\mathbb{X}
$
\mathbb{X}
. We also estimate the total energy of the system over time interval [0, T] for any T > 0, with a tolerance level of the disturbances. Finally, when the input disturbances are insignificant, uniform exponential
stabilization is obtained and an explicit form for the energy decay rate is derived. These results are achieved by a direct
method under undamped mixed boundary conditions. 相似文献
11.
M. S. Agranovich 《Functional Analysis and Its Applications》2009,43(3):165-183
We consider a strongly elliptic second-order system in a bounded n-dimensional domain Ω+ with Lipschitz boundary Γ, n ≥ 2. The smoothness assumptions on the coefficients are minimized. For convenience, we assume that the domain is contained
in the standard torus $
\mathbb{T}^n
$
\mathbb{T}^n
. In previous papers, we obtained results on the unique solvability of the Dirichlet and Neumann problems in the spaces H
p
σ
and B
p
σ
without use of surface potentials. In the present paper, using the approach proposed by Costabel and McLean, we define surface
potentials and discuss their properties assuming that the Dirichlet and Neumann problems in Ω+ and the complementing domain Ω− are uniquely solvable. In particular, we prove the invertibility of the integral single layer operator and the hypersingular
operator in Besov spaces on Γ. We describe some of their spectral properties as well as those of the corresponding transmission
problems. 相似文献
12.
A. V. Stolyarov 《Russian Mathematics (Iz VUZ)》2010,54(11):56-65
In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a
regular hypersurface V
n−1 embedded into a projective-metric space K
n
, n ≥ 3, intrinsically induces a dual projective-metric space $
\bar K_n
$
\bar K_n
. 2) An invariant analytical condition is established under which a normalization of a hypersurface V
n−1 ⊂ K
n
(a tangential hypersurface $
\bar V_{n - 1}
$
\bar V_{n - 1}
⊂ $
\bar K_n
$
\bar K_n
) by quasitensor fields H
n
i
, H
i
($
\bar H_n^i
$
\bar H_n^i
, $
\bar H_i
$
\bar H_i
) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R
n−1 and $
\bar R_{n - 1}
$
\bar R_{n - 1}
are spaces of the same constant curvature $
K = - \tfrac{1}
{c}
$
K = - \tfrac{1}
{c}
. 3) Geometric interpretations of the obtained analytical conditions are given. 相似文献
13.
Gadadhar Misra 《印度理论与应用数学杂志》2010,41(1):189-197
In this note, we point out that a large family of n×n matrix valued kernel functions defined on the unit disc $
\mathbb{D} \subseteq \mathbb{C}
$
\mathbb{D} \subseteq \mathbb{C}
, which were constructed recently in [9], behave like the familiar Bergman kernel function on $
\mathbb{D}
$
\mathbb{D}
in several different ways. We show that a number of questions involving the multiplication operator on the corresponding
Hilbert space of holomorphic functions on $
\mathbb{D}
$
\mathbb{D}
can be answered using this likeness. 相似文献
14.
Stevo Stević 《Siberian Mathematical Journal》2009,50(6):1098-1105
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
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