共查询到20条相似文献,搜索用时 296 毫秒
1.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
2.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
3.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
4.
We consider the perturbed harmonic oscillator
in
, where
is a real-valued potential. We prove that the mapping
spectral data = {eigenvalues of T
D
}
{norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to
is given.
Dedicated to Vladimir Buslaev on the occasion of his 70th birthday
Submitted: September 27, 2006. Accepted: January 9, 2007. 相似文献
5.
Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero 总被引:2,自引:0,他引:2
Under the cancellation property and a certain Dini-type condition
on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous
functions of degree zero, are bounded from
to
,
from
to
, and from
to
for
. 相似文献
6.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
7.
Özgür Ceyhan 《Selecta Mathematica, New Series》2007,13(2):203-237
The moduli space parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex
generated by the fundamental classes of strata of . We show that the homology of is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of .
相似文献
8.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献
9.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
10.
Adimurthi K. Sandeep 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):585-603
Let Ω be a bounded domain in
, we prove the singular Moser-Trudinger embedding:
if and only if
where
and
. We will also study the corresponding critical exponent problem. 相似文献
11.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
12.
Let
be the L
2-critical nonlinear Schr?dinger equation, in a domain
with initial data in
(Dirichlet boundary condition) and
. We prove existence and stability of finite time blow-up dynamics with the log-log blow-up speed
Moreover, for a suitable class of finite time blow-up solutions, we derive global rigidity properties which turn out to be
modeled after the
ones.
Submitted: October 14, 2005. Revised: October 26, 2006. Accepted: February 2, 2007. 相似文献
13.
F. Brackx H. De Schepper N. De Schepper F. Sommen 《Advances in Applied Clifford Algebras》2007,17(3):311-330
Orthogonal Clifford analysis in flat m–dimensional Euclidean space focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued
Dirac operator
, where (
) forms an orthogonal basis for the quadratic space
underlying the construction of the Clifford algebra
. When allowing for complex constants and taking the dimension to be even: m = 2n, the same set of generators produces the complex Clifford algebra
, which we equip with a Hermitean Clifford conjugation and a Hermitean inner product. Hermitean Clifford analysis then focusses
on the simultaneous null solutions of two mutually conjugate Hermitean Dirac operators, naturally arising in the present context
and being invariant under the action of a realization of the unitary group U (n). In this so–called Hermitean setting Clifford–Hermite polynomials are constructed, starting from a Rodrigues formula involving
both Dirac operators mentioned. Due to the specific features of the Hermitean setting, four different types of polynomials
are obtained, two types of even degree and two types of odd degree. We investigate their properties: recurrence relations,
structure, explicit form and orthogonality w.r.t. a deliberately chosen weight function. They also give rise to the definition
of the Hermitean Clifford–Hermite functions, and may be used to develop a Hermitean continuous wavelet transform, see [4]. 相似文献
14.
Christian Richter 《Journal of Geometry》2006,84(1-2):117-132
Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday 相似文献
15.
16.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
17.
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
18.
19.
Huoxiong Wu 《Integral Equations and Operator Theory》2005,52(2):285-298
This paper is devoted to the study on the Lp-mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on
The
boundedness of the Marcinkiewicz integrals for some fixed 1 < p < ∞ are obtained under some size conditions, which essentially improve or extend some well-known results. 相似文献
20.
We extend the results for 2-D Boussinesq equations from ℝ2 to a bounded domain Ω. First, as for the existence of weak solutions, we transform Boussinesq equations to a nonlinear evolution
equation U
t
+ A(t, U) = 0. In stead of using the methods of fundamental solutions in the case of entire ℝ2, we study the qualities of F(u, υ) = (u · ▽)υ to get some useful estimates for A(t, U), which helps us to conclude the local-in-time existence and uniqueness of solutions. Second, as for blow-up criterions,
we use energy methods, Sobolev inequalities and Gronwall inequality to control
and
by
and
. Furthermore,
can control
by using vorticity transportation equations. At last,
can control
. Thus, we can find a blow-up criterion in the form of
.
相似文献