共查询到20条相似文献,搜索用时 18 毫秒
1.
E. S. Dubtsov 《Journal of Mathematical Sciences》2010,165(4):449-454
Let
\mathbbD \mathbb{D}
n
denote the unit polydisk and let B
n
denote the unit ball in
\mathbbC \mathbb{C}
n
, n ≥1. We study weighted composition operators on the α-Bloch spaces Ba {\mathcal{B}^\alpha } (
\mathbbD \mathbb{D}
n
), α > 1. We also study Cesàro type operators on the α-Bloch spaces Ba {\mathcal{B}^\alpha } (B
n
), α > 0. Bibliography: 15 titles. 相似文献
2.
We study the limiting behavior of the K?hler–Ricci flow on
\mathbbP(O\mathbbPn ?O\mathbbPn(-1)?(m+1)){{\mathbb{P}(\mathcal{O}_{\mathbb{P}^n} \oplus \mathcal{O}_{\mathbb{P}^n}(-1)^{\oplus(m+1)})}} for m, n ≥ 1, assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses
to
\mathbbPn{{\mathbb{P}^n}} or contracts a subvariety of codimension m + 1 in the Gromov–Hausdorff sense. We also show that the K?hler–Ricci flow resolves a certain type of cone singularities
in the Gromov–Hausdorff sense. 相似文献
3.
In 1998, Kleinbock and Margulis proved Sprindzuk’s conjecture pertaining to metrical Diophantine approximation (and indeed
the stronger Baker–Sprindzuk conjecture). In essence, the conjecture stated that the simultaneous homogeneous Diophantine
exponent w
0(x) = 1/n for almost every point x on a nondegenerate submanifold M \mathcal{M} of
\mathbbRn {\mathbb{R}^n} . In this paper, the simultaneous inhomogeneous analogue of Sprindzuk’s conjecture is established. More precisely, for any
“inhomogeneous” vector θ ∈
\mathbbRn {\mathbb{R}^n} we prove that the simultaneous inhomogeneous Diophantine exponent w
0(x
,
θ) is 1/n for almost every point x on M \mathcal{M} . The key result is an inhomogeneous transference principle which enables us to deduce that the homogeneous exponent w
0(x) is 1/n for almost all x ∈ M \mathcal{M} if and only if, for any θ ∈
\mathbbRn {\mathbb{R}^n} , the inhomogeneous exponent w
0(x
,
θ) = 1/n for almost all x ∈ M \mathcal{M} . The inhomogeneous transference principle introduced in this paper is an extremely simplified version of that recently discovered
by us. Nevertheless, it should be emphasised that the simplified version has the great advantage of bringing to the forefront
the main ideas while omitting the abstract and technical notions that come with describing the inhomogeneous transference
principle in all its glory. 相似文献
4.
We consider a family of operators Hγμ(k), k ∈
\mathbbTd \mathbb{T}^d := (−π,π]d, associated with the Hamiltonian of a system consisting of at most two particles on a d-dimensional lattice ℤd, interacting via both a pair contact potential (μ > 0) and creation and annihilation operators (γ > 0). We prove the existence of a unique eigenvalue of Hγμ(k), k ∈
\mathbbTd \mathbb{T}^d , or its absence depending on both the interaction parameters γ,μ ≥ 0 and the system quasimomentum k ∈
\mathbbTd \mathbb{T}^d . We show that the corresponding eigenvector is analytic. We establish that the eigenvalue and eigenvector are analytic functions
of the quasimomentum k ∈
\mathbbTd \mathbb{T}^d in the existence domain G ⊂
\mathbbTd \mathbb{T}^d . 相似文献
5.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
6.
Boris Širola 《Central European Journal of Mathematics》2011,9(6):1317-1332
Let
\mathbbK\mathbb{K} be a field, G a reductive algebraic
\mathbbK\mathbb{K}-group, and G
1 ≤ G a reductive subgroup. For G
1 ≤ G, the corresponding groups of
\mathbbK\mathbb{K}-points, we study the normalizer N = N
G
(G
1). In particular, for a standard embedding of the odd orthogonal group G
1 = SO(m,
\mathbbK\mathbb{K}) in G = SL(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊ μ
m
(
\mathbbK\mathbb{K}), the semidirect product of G
1 by the group of m-th roots of unity in
\mathbbK\mathbb{K}. The normalizers of the even orthogonal and symplectic subgroup of SL(2n,
\mathbbK\mathbb{K}) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof
in the odd orthogonal case to be completed here. Also, for G = GL(m,
\mathbbK\mathbb{K}) and G
1 = O(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊
\mathbbK\mathbb{K}
×. In both of these cases, N is a self-normalizing subgroup of G. 相似文献
7.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
Cr([`(\mathbbD)]n;\mathbb C) = {f:[`(\mathbbD)]n? \mathbb C:f is continuous and f(z)=[`(f([`(z)]))] (z ? [`(\mathbbD)]n)}C_{\rm r}(\overline{\mathbb{D}}^n;\mathbb {C}) =\left\{f: \overline{\mathbb{D}}^n\rightarrow \mathbb {C}:f \,\, {\rm is \,\, continuous \,\, and}\,\, f(z)=\overline{f(\overline{z})} \;(z\in \overline{\mathbb{D}}^n)\right\} 相似文献
8.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
9.
Christopher Kennedy 《Algebras and Representation Theory》2011,14(6):1187-1202
This paper continues the study of associative and Lie deep matrix algebras,
DM(X,\mathbbK){\mathcal{DM}}(X,{\mathbb{K}}) and
\mathfrakgld(X,\mathbbK){\mathfrak{gld}}(X,{\mathbb{K}}), and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras,
BDM(X,\mathbbK){\mathcal{BDM}}(X,{\mathbb{K}}) and
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}), are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal
lattices. In particular,
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) is shown to be semisimple. The Lie algebra
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct
product of
\mathfraksln{\mathfrak{{sl}_n}}’s. We classify all associative bilinear forms on
\mathfraksl2\mathfrakd{\mathfrak{sl}_2\mathfrak{d}} (a natural depth analogue of
\mathfraksl2{\mathfrak{{sl}_2}}) and
\mathfrakbld{\mathfrak{bld}}. 相似文献
10.
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter–Reissner–Nordstr?m black holes.
We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering
matrix S(λ) at a fixed energy λ ≠ 0. More precisely, we consider the partial wave scattering matrices S(λ, n) (here λ ≠ 0 is the fixed energy and
n ? \mathbbN*{n \in \mathbb{N}^{*}} denotes the angular momentum) defined as the restrictions of the full scattering matrix on a well chosen basis of spin-weighted
spherical harmonics. We prove that the mass M, the square of the charge Q
2 and the cosmological constant Λ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge
of either the transmission coefficients T(λ, n), or the reflexion coefficients R(λ, n) (resp. L(λ, n)), for all n ? L{n \in {\mathcal{L}}} where L{\mathcal{L}} is a subset of
\mathbbN*{\mathbb{N}^{*}} that satisfies the Müntz condition
?n ? L\frac1n = +¥{\sum_{n \in{\mathcal{L}}}\frac{1}{n} = +\infty} . Our main tool consists in complexifying the angular momentum n and in studying the analytic properties of the “unphysical” scattering matrix S(λ, z) in the complex variable z. We show, in particular, that the quantities
\frac1T(l,z){\frac{1}{T(\lambda,z)}},
\fracR(l,z)T(l,z){\frac{R(\lambda,z)}{T(\lambda,z)}} and
\fracL(l,z)T(l,z){\frac{L(\lambda,z)}{T(\lambda,z)}} belong to the Nevanlinna class in the region ${\{z \in \mathbb{C}, Re(z) > 0 \}}${\{z \in \mathbb{C}, Re(z) > 0 \}} for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstruction
formulae for the surface gravities of the event and cosmological horizons of the black hole which have an important physical
meaning in the Hawking effect. 相似文献
11.
S. S. Gribkova 《Journal of Mathematical Sciences》2010,167(4):506-511
Let x(t),t ? [ 0,1 ] \xi (t),t \in \left[ {0,1} \right] , be a jump Lévy process. By Px {\mathcal{P}_\xi } we denote the law of in the Skorokhod space
\mathbbD {\mathbb{D}} [0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of Px {\mathcal{P}_\xi } -preserving transformations of the space
\mathbbD {\mathbb{D}} [0, 1]. Bibliography: 10 titles. 相似文献
12.
Szymon Gła̧b 《Central European Journal of Mathematics》2009,7(4):732-740
Let $
\mathcal{K}
$
\mathcal{K}
(ℝ) stand for the hyperspace of all nonempty compact sets on the real line and let d
±(x;E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ ℝ at a point x∈ ℝ. In [3] it was proved that
|