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1.
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
2.
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
3.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
4.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
5.
In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold
M of dimension six and codimension two, i.e. a pair
, consisting of a principal bundle
over M and of a Cartan connection form
over P, satisfying the following property: the (local) CR transformations
are in one to one correspondence with the (local) automorphisms
for which
. For any
, this construction determines an explicit monomorphism of the stability subalgebra Lie (Aut(M)x) into the Lie algebra
of the structure group H of P.
Mathematics Subject Classification (2000) Primary 32V05, Secondary 53C15, 53A55 相似文献
6.
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
7.
Let L and M be Archimedean vector lattices such that
and
are complex vector lattices. We constructively and intrinsically prove that if
is an order bounded disjointness preserving operator from
into
then the modulus
of
exists in the ordered vector space of all order bounded operators from L into M.
Received February 11, 2005; accepted in final form March 8, 2005. 相似文献
8.
C. Mendes 《Algebra Universalis》2005,54(3):279-290
An Ockham algebra
that satisfies the identity
is called a Kn, m-algebra. Generalizing some results obtained in [2], J. Varlet and T. Blyth, in [3, Chapter 8], study congruences on K1, 1-algebras. In particular, they describe the complement (when it exists) of a principal congruence and characterize these congruences
that are complemented. In this paper we study the same question for Kn, m-algebras.
Received March 24, 2005; accepted in final form April 28, 2005. 相似文献
9.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
10.
Bhagwati Prashad Duggal Slavisa V. Djordjević 《Mediterranean Journal of Mathematics》2005,2(4):395-406
It is known that if
and
are Banach space operators with the single-valued extension property, SVEP, then the matrix operator
has SVEP for every operator
and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M0 ensuring Weyls theorem for operators MC. 相似文献
11.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
12.
Birkhoff coordinates for KdV on phase spaces of distributions 总被引:1,自引:0,他引:1
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space
of square integrable 1-periodic functions with mean value zero to the phase space
of mean value zero distributions from the Sobolev space
endowed with the symplectic structure
More precisely, we construct a globally defined real-analytic symplectomorphism
where
is a weighted Hilbert space of sequences
supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in
is a function of the actions
alone. 相似文献
13.
Hans-Peter Schröcker 《Journal of Geometry》2005,82(1-2):172-187
We study the projective space
of univariate rational parameterized equations of degree d or less in real projective space
The parameterized equations of degree less than d form a special algebraic variety
We investigate the subspaces on
and their relation to rational curves in
give a geometric characterization of the automorphism group of
and outline applications of the theory to projective kinematics. 相似文献
14.
George M. Bergman 《Algebra Universalis》2005,53(2-3):357-395
Properties of several sorts of lattices of convex subsets of
are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of
and the lattice of all convex subsets of
The lattices of arbitrary, of open bounded, and of compact convex sets in
all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set
satisfies some, but in general not all of the identities of the lattice of “genuine” convex subsets of
To the memory of Ivan RivalReceived April 22, 2003; accepted in final form February 16, 2005.This revised version was published online in August 2005 with a corrected cover date. 相似文献
15.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献
16.
Naser Zamani 《Archiv der Mathematik》2006,86(4):321-330
Let
be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let
denote the i-th graded generalized local cohomology of N relative to M with support in
. We study the vanishing, tameness and asymptotical stability of the homogeneous components of
.
Received: 22 March 2005; revised: 25 June 2005 相似文献
17.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
18.
We show that if A is a separable, nuclear,
-absorbing (or strongly purely infinite) C*-algebra which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form
where Γ is a finite connected graph (and
is the algebra of continuous functions on Γ that vanish at a distinguished point
).We show further that if B is any separable, nuclear C*-algebra, then
is isomorphic to a crossed product
where D is an inductive limit of C*-algebras of the form
(and D is
-absorbing and homotopic to zero in an ideal-system preserving way).Received: December 2003 Revision: July 2004 Accepted: July 2004 相似文献
19.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
20.
Let p be a prime,
a finite p-group,
any finite group with order divisible by p,
and
any action of
on
. We show that the cardinality of the set of all derivations
with respect to this action is a multiple of
p. This
generalises theorems of Frobenius and Hall.
Received: 16 June 2003 相似文献