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1.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
2.
Given a continuous linear operator T L(x) defined on a separable
-space X, we will show that T satisfies the Hypercyclicity Criterion if and only if for any strictly increasing sequence of positive integers
such that
the sequence
is hypercyclic. In contrast we will also prove that, for any hypercyclic vector x X of T, there exists a strictly increasing sequence
such that
and
is somewhere dense, but not dense in X. That is, T and
do not share the same hypercyclic vectors. 相似文献
3.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
4.
Hui-qiong Li Zhen-long Chenu 《应用数学学报(英文版)》2007,23(4):579-592
Let{(t);t∈R_ ~N}be a d-dimensional N-parameter generalized Brownian sheet.Necessaryand sufficient conditions for a compact set E×F to be a polar set for(t,(t))are proved.It is also provedthat if 2N≤αd,then for any compact set ER_>~N,d-2/2 Dim E≤inf{dimF:F ∈ B(R~d),P{(E)∩F≠φ}>0}≤d-2/β DimE,and if 2N>αd,then for any compact set FR~d\{0},α/2(d-DimF)≤inf{dimE:E∈B(R_>~N),P{(E)∩F≠φ}>0}≤β/2(d-DimF),where B(R~d)and B(R_>~N)denote the Borel σ-algebra in R~d and in R_>~N respectively,dim and Dim are Hausdorffdimension and Packing dimension respectively. 相似文献
5.
For an arbitrary set E and a given closure operator
, we want to construct a symmetric closure operator
via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator .
defines a matroid. If
and
is the convex closure operator,
turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by
visibility.
Received March 9, 2005 相似文献
6.
In this paper, we will give some optimal estimates on the rotation number of the linear equation
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,
and that of the asymmetric equation:
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,
where p(t) and q(t) are almost periodic functions and
x + = max{ x,0} , x - = min{ x,0} .x_{ + } = \max \{ x,0\} ,\;x_{ - } = \min \{ x,0\} .
These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions. 相似文献
7.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
8.
9.
We establish a new 3G-Theorem for the Green’s function for the half space
We exploit this result to introduce a new class of potentials
that we characterize by means of the Gauss semigroup on
. Next, we define a subclass
of
and we study it. In particular, we prove that
properly contains the classical Kato class
. Finally, we study the existence of positive continuous solutions in
of the following nonlinear elliptic problem
where h is a Borel measurable function in
satisfying some appropriate conditions related to the class
.
Mathematics Subject Classification (1991): Primary: 34B27, 34B16, 34J65; Secondary: 35B50, 31B05 相似文献
10.
Chaohui ZHANG 《数学年刊B辑(英文版)》2007,28(1):55-66
Let S be a Riemann surface with genus p and n punctures. Assume that 3p - 3 n > 0 and n ≥ 1. Let a be a puncture of S and let (~S) = S ∪ {a}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod(~S) under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mod(~S). 相似文献
11.
In this paper, we continue our investigation on “Extremal problems under dimension constraints” introduced [1]. The general problem we deal with in this paper can be formulated as follows. Let
be an affine plane of dimension k in
. Given
determine or estimate
.Here we consider and solve the problem in the special case where
is a hyperplane in
and the “forbidden set”
. The same problem is considered for the case, where
is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.AMS Classification: 05C35, 05B30, 52C99 相似文献
12.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
13.
This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
相似文献
14.
We study holomorphic flows on Stein manifolds. We prove that a holomorphic flow with isolated singularities and a dicritical
singularity of the form
on a Stein manifold
with
, is globally analytically linearizable; in particular M is biholomorphic to
. A complete stability result for periodic orbits is also obtained.
Bruno Scárdua: Partially supported by ICTP-Trieste-Italy.
Received: 27 September 2006 相似文献
15.
16.
The optimal value function
of the quadratic program
, where
is a given symmetric matrix,
a given matrix,
and
are the linear perturbations, is considered. It is proved that
is directionally differentiable at any point
in its effective domain
. Formulae for computing the directional derivative
of
at
in a direction
are obtained. We also present an example showing that, in general,
is not piecewise linear-quadratic on W. The preceding (unpublished) example of Klatte is also discussed. 相似文献
17.
Pei Yuan Wu 《Integral Equations and Operator Theory》2006,56(4):559-569
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if
, where U is a singular unitary operator with multiplicity
and x1, . . . , xd are orthonormal vectors satisfying
. For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors. 相似文献
18.
M. Rovinsky 《Selecta Mathematica, New Series》2005,11(3-4):491-522
Let L be the function field of a projective space
over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf
on
is a collection of isomorphisms
for each g ∈ H satisfying the chain rule.
We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semilinear representations of H extendable to the semigroup End(L/k) to the category of coherent H-sheaves on
The paper is motivated by a study of admissible representations of the automorphism group G of an algebraically closed extension of k of countable transcendence degree undertaken in [4]. The semigroup End(L/k) is considered as a subquotient of G, hence the condition on extendability.
In the appendix it is shown that, if
is either H, or a bigger subgroup in the Cremona group (generated by H and a certain pair of involutions), then any semilinear
of degree one is an integral L-tensor power of
It is also shown that this bigger subgroup has no non-trivial representations of finite degree if n > 1. 相似文献
19.