共查询到20条相似文献,搜索用时 31 毫秒
1.
Giovanni Colombo Antonio Marigonda 《Calculus of Variations and Partial Differential Equations》2006,25(1):1-31
Closed sets K ⊂
satisfying an external sphere condition with uniform radius (called ϕ-convexity or proximal smoothness) are considered. It
is shown that for
-a.e. x ∊ ∂K the proximal normal cone to K at x has dimension one. Moreover if K is the closure of an open set satisfying a (sharp) nondegeneracy condition, then the De Giorgi reduced boundary is equivalent
to ∂ K and the unit proximal normal equals
-a.e. the (De Giorgi) external normal. Then lower semicontinuous functions f :
with ϕ-convex epigraph are shown, among other results, to be locally BV and twice
-a.e. differentiable; furthermore, the lower dimensional rectifiability of the singular set where f is not differentiable is studied. Finally we show that for
-a.e. x there exists δ (x) > 0 such that f is semiconvex on B(x,δ(x)). We remark that such functions are neither convex nor locally Lipschitz, in general. Methods of nonsmooth analysis and
of geometric measure theory are used.
Work partially supported by M.I.U.R., project “Viscosity, metric, and control theoretic methods for nonlinear partial differential
equations.” 相似文献
2.
Olympia Talelli 《Archiv der Mathematik》2007,89(1):24-32
We define a group G to be of type Φ if it has the property that for every
-module G, proj.
G < ∞ iff proj.
H G < ∞ for every finite subgroup H of G. We conjecture that the type Φ is an algebraic characterization of those groups G which admit a finite dimensional model for
, the classifying space for the family of the finite subgroups of G. We also conjecture that the type Φ is equivalent to spli being finite, where spli
is the supremum of the projective lengths of the injective
-modules. Here we prove certain parts of these conjectures.
The project is cofounded by the European Social Fund and National Resources–EPEAK II–Pythagoras.
Received: 21 June 2006 相似文献
3.
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
4.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
5.
Fredholm conditions and an index formula are obtained for Wiener-Hopf operators W(a) with slowly oscillating matrix symbols a on weighted Lebesgue spaces where 1 < p < ∞, w is a Muckenhoupt weight on and . The entries of matrix symbols belong to a Banach subalgebra of Fourier multipliers on that are continuous on and have, in general, different slowly oscillating asymptotics at ±∞. To define the Banach algebra SOp, w of corresponding slowly oscillating functions, we apply the theory of pseudodifferential and Calderón-Zygmund operators.
Established sufficient conditions become a Fredholm criterion in the case of Muckenhoupt weights with equal indices of powerlikeness,
and also for Muckenhoupt weights with different indices of powerlikeness under some additional condition on p, w and a.
Work was supported by the SEP-CONACYT Project No. 25564 (México). The second author was also sponsored by the CONACYT scholarship
No. 163480. 相似文献
6.
Let W(ψ) denote the set of ψ-well approximable points in
and let K be a compact subset of
which supports a measure μ. In this short article, we show that if μ is an ‘absolutely friendly’ measure and a certain μ-volume
sum converges then
The result obtained is in some sense analogous to the convergence part of Khintchine’s classical theorem in the theory of
metric Diophantine approximation. The class of absolutely friendly measures is a subclass of the friendly measures introduced
in [2] and includes measures supported on self-similar sets satisfying the open set condition. We also obtain an upper bound
result for the Hausdorff dimension of
相似文献
7.
Jing YANG Shi Xin LUO Ke Qin FENG 《数学学报(英文版)》2006,22(3):833-844
Assume that m ≥ 2, p is a prime number, (m,p(p - 1)) = 1,-1 not belong to 〈p〉 belong to (Z/mZ)^* and [(Z/mZ)^*:〈p〉]=4.In this paper, we calculate the value of Gauss sum G(X)=∑x∈F^*x(x)ζp^T(x) over Fq,where q=p^f,f=φ(m)/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G(x) belongs to the decomposition field K of p in Q(ζm) and K is an imaginary quartic abelian unmber field.When the Galois group Gal(K/Q) is cyclic,we have studied this cyclic case in anotyer paper:"Gauss sums of index four:(1)cyclic case"(accepted by Acta Mathematica Sinica,2003).In this paper we deal with the non-cyclic case. 相似文献
8.
We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on
for
or
and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in
or
相似文献
9.
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
10.
In this paper for a positive real number α we consider two partial differential operators D and Dα on the half–plane
We define a generalized Fourier transform
associated with the operators D and Dα. We establish an analogue of Beurling–H?rmander’s Theorem for this transform
and we give some applications of this theorem. 相似文献
11.
Let
be open sets, let A (resp. B) be a subset of the boundary ∂D (resp. ∂G) and let W be the 2-fold boundary cross
. An open subset
is said to be the “envelope of holomorphy” of W if it is, in some sense, the maximal open set with the following property: Any function locally bounded on W and separately holomorphic on
“extends” to a holomorphic function defined on X which admits the boundary values f a.e. on W. In this work we will determine the envelope of holomorphy of some boundary crosses.
Received: 12 October 2006 相似文献
12.
Summary.
Let
be a field of real or complex numbers and
denote the set of nonzero elements of
.
Let
be an abelian group. In this paper, we solve the functional equation
f
1
(x +
y) +
f
2
(x -
y) =
f
3
(x) +
f
4
(y) +
g(xy)
by modifying the domain of the unknown functions
f
3,
f
4, and
g from
to
and using a method different from [3]. Using this result,
we determine all functions
f
defined on
and taking values on
such that the difference
f(x + y) + f
(x -
y) - 2
f(x) - 2
f(y)
depends only on the product
xy for all
x and
y in
相似文献
13.
Heinz Langer Alexander Markus Vladimir Matsaev 《Integral Equations and Operator Theory》2009,63(4):533-545
In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ0 and is boundedly invertible in the endpoints of Δ0, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ0 and a so-called inner linearization of the operator function A(z) in the subspace are established.
相似文献
14.
Let
, n ≥ 2, be the near 2n-gon on the 2-factors of a complete graph with 2n + 2 vertices. In this paper, we classify the valuations of the near octagon
. We use this classification to study isometric full embeddings of
into DQ(8,2) and DH(7,4). We show that there is up to isomorphism a unique isometric full embedding of
into each of these dual polar spaces. Further applications are expected in the classification of dense near polygons with
lines of size 3. 相似文献
15.
Xiong Ping DAI 《数学学报(英文版)》2006,22(1):301-310
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles 相似文献
16.
Souček [1, 2] discovered an intriguing connection between the standard twistor correspondence and the biquaternionic projective
line
The biquaternionic projective point,
also has twistor structure corresponding to the collection of α- or β-planes passing through the origin in spacetime. The
duality between α- or β-planes is shown to correspond to the choice of left vs. right scalar action. Moreover, we find that
is homeomorphic to the scheme
相似文献
17.
J. J. Grobler 《Integral Equations and Operator Theory》2007,57(1):83-99
For a probability space
we denote the marginal measures of
, defined on Σ and Λ respectively, by
and
. If ρ is a function norm defined on
marginal function norms ρ1 and ρ2 are defined on
and
. We find conditions which guarantee Lρ 1 + Lρ 2 to be embedded in Lρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals.
We find a condition which, applied to the binormal distribution in L2, improves some known conditions. 相似文献
18.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献
19.
Fazli Kh 《Statistical Inference for Stochastic Processes》2007,10(2):181-208
We observe a realization X
(n) of a Poisson process on the set
with intensity function
depending on the unknown real parameter
. Based on X
(n) we test simple null hypothesis
against one sided alternative
for given
. We improve the level of the well-known locally asymptotically uniformly most powerful (LAUMP) test by using the Edgeworth
type expansion for stochastic integral. We show that the improved test is second-order efficient under certain regularity
conditions.
相似文献
20.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献