共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
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
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.
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
5.
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
6.
We classify deformations of the standard embedding of the Lie superalgebra $
\mathcal{K}
$
\mathcal{K}
(2) of contact vector fields on the (1, 2)-dimensional supercircle into the Lie superalgebra SΨD(S
1|2
) of pseudodifferential operators on the supercircle S
1|2
. The proposed approach leads to the deformations of the central charge induced on $
\mathcal{K}
$
\mathcal{K}
(2) by the canonical central extension of SΨD(S
1|2
). 相似文献
7.
Viorel Vâjâitu 《Czechoslovak Mathematical Journal》2010,60(3):655-667
Let X be a complex space of dimension n, not necessarily reduced, whose cohomology groups H
1(X, $
\mathcal{O}
$
\mathcal{O}
), ...,H
n−1(X, $
\mathcal{O}
$
\mathcal{O}
) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1-convex) if, and only if, X is holomorphically
spreadable (resp., X is holomorphically spreadable at infinity). 相似文献
8.
A. Olofsson 《Acta Mathematica Hungarica》2010,128(3):265-286
We develop a Wold decomposition for the shift semigroup on the Hardy space $
\mathcal{H}^2
$
\mathcal{H}^2
of square summable Dirichlet series convergent in the half-plane $
\Re (s) > 1/2
$
\Re (s) > 1/2
. As an application we have that a shift invariant subspace of $
\mathcal{H}^2
$
\mathcal{H}^2
is unitarily equivalent to $
\mathcal{H}^2
$
\mathcal{H}^2
if and only if it has the form $
\phi \mathcal{H}^2
$
\phi \mathcal{H}^2
for some $
\mathcal{H}^2
$
\mathcal{H}^2
-inner function φ. 相似文献
9.
Philip J. Maher 《Rendiconti del Circolo Matematico di Palermo》2010,59(1):53-65
In this paper we extend to C*-algebras and to von Neumann algebras some results on approximants that have previously been found in the context of $
\mathcal{L}
$
\mathcal{L}
(H) and of the von Neumann-Schatten classesC
p
, 1⩽ p <∞. We obtain results concerning positive approximants, unitary and partially isometric approximants and commutator approximants;
and we study paranormality. Our main tools are the Gelfand-naimark Theorem and Berntzen’s results on normal spectral approximation. 相似文献
10.
The bipartite density of a graph G is max {|E(H)|/|E(G)|: H is a bipartite subgraph of G}. It is NP-hard to determine the bipartite density of any triangle-free cubic graph. A biased maximum bipartite subgraph of a graph G is a bipartite subgraph of G with the maximum number of edges such that one of its partite sets is independent in G. Let $
\mathcal{H}
$
\mathcal{H}
denote the collection of all connected cubic graphs which have bipartite density $
\tfrac{4}
{5}
$
\tfrac{4}
{5}
and contain biased maximum bipartite subgraphs. Bollobás and Scott asked which cubic graphs belong to $
\mathcal{H}
$
\mathcal{H}
. This same problem was also proposed by Malle in 1982. We show that any graph in $
\mathcal{H}
$
\mathcal{H}
can be reduced, through a sequence of three types of operations, to a member of a well characterized class. As a consequence,
we give an algorithm that decides whether a given graph G belongs to $
\mathcal{H}
$
\mathcal{H}
. Our algorithm runs in polynomial time, provided that G has a constant number of triangles that are not blocks of G and do not share edges with any other triangles in G. 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.
Let $
\mathfrak{S}
$
\mathfrak{S}
be a locally compact semigroup, ω be a weight function on $
\mathfrak{S}
$
\mathfrak{S}
, and M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) be the weighted semigroup algebra of $
\mathfrak{S}
$
\mathfrak{S}
. Let L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) be the C*-algebra of all M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)-measurable functions g on $
\mathfrak{S}
$
\mathfrak{S}
such that g/ω vanishes at infinity. We introduce and study a strict topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) and show that the Banach space L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) can be identified with the dual of M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) endowed with β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω). We finally investigate some properties of the locally convex topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω). 相似文献
13.
Hongliang Yao 《Proceedings Mathematical Sciences》2010,120(2):199-207
Lin and Su classified A$
\mathcal{T}
$
\mathcal{T}
-algebras of real rank zero. This class includes all A$
\mathbb{T}
$
\mathbb{T}
-algebras of real rank zero as well as many C*-algebras which are not stably finite. An A$
\mathcal{T}
$
\mathcal{T}
-algebra often becomes an extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra which is not an A$
\mathcal{T}
$
\mathcal{T}
-algebra. We describe a characterization of an extension E of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra if E is an A$
\mathcal{T}
$
\mathcal{T}
-algebra. 相似文献
14.
Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in
a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized
Fresnel class $
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
$
\mathcal{F}_{\mathcal{A}_1 ,\mathcal{A}_2 }
A1,A2 than the Fresnel class $
\mathcal{F}
$
\mathcal{F}
(B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener
space having the form
|