共查询到20条相似文献,搜索用时 46 毫秒
1.
Let
C( \mathbbRm ) C\left( {{\mathbb{R}^m}} \right) be the space of bounded and continuous functions
x:\mathbbRm ? \mathbbR x:{\mathbb{R}^m} \to \mathbb{R} equipped with the norm
|| x ||C = || x ||C( \mathbbRm ): = sup{ | x(t) |:t ? \mathbbRm } \left\| x \right\|C = {\left\| x \right\|_{C\left( {{\mathbb{R}^m}} \right)}}: = \sup \left\{ {\left| {x(t)} \right|:t \in {\mathbb{R}^m}} \right\} 相似文献
2.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
3.
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
4.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
5.
Let X, X
1, X
2,… be i.i.d.
\mathbbRd {\mathbb{R}^d} -valued real random vectors. Assume that E
X = 0 and that X has a nondegenerate distribution. Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms
\mathbbQ[ SN ] \mathbb{Q}\left[ {{S_N}} \right] of the normalized sums S
N
= N
−1/2 (X
1 + ⋯ + X
N
) and show that, without any additional conditions,
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