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1.
Let
and
be a perturbed eigenpair of a diagonalisable matrixA. The problem is to bound the error in
and
. We present one absolute perturbation bound and two relative perturbation bounds.
The absolute perturbation bound is an extension of Davis and Kahan's sin θ Theorem from Hermitian to diagonalisable matrices.
The two relative perturbation bounds assume that
and
are an exact eigenpair of a perturbed matrixD
1
AD
2
, whereD
1 andD
2 are non-singular, butD
1
AD
2 is not necessarily diagonalisable. We derive a bound on the relative error in
and a sin θ theorem based on a relative eigenvalue separation. The perturbation bounds contain both the deviation ofD
1 andD
2 from similarity and the deviation ofD
2 from identity.
This work was partially supported by NSF grant CCR-9400921. 相似文献
2.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
3.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
4.
S. Mecheri 《Journal of Mathematical Sciences》2000,102(5):4429-4435
A generalized derivation
, is defined by the formula
, where
and
is the Banach algebra of bounded linear operators in a Hilbert space
. Sufficient conditions under which
and
are given. Bibliography: 8 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 111–119. 相似文献
5.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
6.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
7.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
8.
Let Δ(1) be the uniform three direction mesh of the plane whose vertices are integer points of
.Let
(respectively
of degree d=3r (respectively d=3r+1 ) for r odd (respectively even) on the triangulation
, and of degree d=2r (respectively d=2r+1) for r odd (respectively even) on the triangulation
. Using linear combinations of translates of these splines we obtain Lagrange interpolants whose corresponding order of approximation
is optimal.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of
-modules, theresidue complex
. These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex
is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes,
and
, which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical
dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms. 相似文献
10.
We introduce the notion of a generalized interval exchange
induced by a measurable k-partition
of [0,1).
can be viewed as the corresponding restriction of a nondecreasing function
on ℝ with
. A is called λ-dense if λ(A
i
∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that
. We give necessary and sufficient conditions for this equality to hold. We show that for each integer m≥2, such that 3∤2m+1, there exist 2 and 3 non λ-dense partitions A and B of [0,1), corresponding to the interval exchanges on 2m intervals, for which
and
commute. 相似文献
11.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
12.
G. A. Margulis 《Geometriae Dedicata》1991,37(1):1-7
Let G be a connected Lie group, let Γ be a lattice in G, and let
be a unipotent subgroup of G. It is proved that, for the natural action of
on G/Γ, every minimal closed
-invariant subset is compact.
Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthday 相似文献
13.
Andrew J. Sommese 《Milan Journal of Mathematics》1997,67(1):49-75
Let
be an algebraic submanifold of complex projective space ℙ
N
. Assume thatn:=dim
and let
denote the restriction of the hyperplane section bundle
to
. The meromorphic map
associated to
fork≥1 ties together the pluricanonical maps of the surface sections of
. Known results show that the behavior of
is far better than one would expect from experience with the pluricanonical mappings of algebraic surfaces. In this article
we discuss the known results on the structure of the mappings
and describe the open problems.
Conferenza tenuta il 5 giugno 1997 相似文献
14.
Summary A nonconforming mixed finite element method is presented for approximation of w with w=f,w|
r
=0. Convergence of the order
is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed. 相似文献
15.
Fabio Vlacci 《Journal d'Analyse Mathématique》1998,75(1):51-66
We introduce the notion of pointwise regularity (
) of Colombeau’s generalized functions and give comparison theorems between
regularity,
- andC
∞-regularity. We also define the notion of a pointwise wave front set and establish a theorem concerning the effect of a linear
generalized partial differential operator on such a wave front. 相似文献
16.
Moshe Dubiner 《Journal d'Analyse Mathématique》1995,67(1):39-116
We consider the problem of polynomial approximation to a real valued functionf defined on a compact set
. An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional
Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional
Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including
for 0<q≤∞.
We have found that the space of polynomials ℙ on a compact setX induces a semimetric
which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to
suffices for the rough theory presented here. Many examples of sets
and their metrics are presented. 相似文献
17.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
18.
John F. Toland 《Arkiv f?r Matematik》2001,39(2):383-394
Let
denote the Hardy space of real-valued functions on the unit circle with weak derivatives in the usual real Hardy space
. It is shown that when the weak derivative of a locally Lipschitz continuous functionf has bounded variation on compact sets the Nemytskii operatorF, defined byF(u)=f·u, maps
continuously into itself. A further condition sufficient for the continuous Fréchet differentiability ofF is then added. 相似文献
19.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
20.
Let K be a field and
a non-trivial valuation ring of K withm as its maximal ideal. Denote by
and
the rings of polynomials f∈K[X] and rational functions f∈K(X) resp. such that
. We prove that for one variable X we have
if and only if the completion of (K,
) is locally compact or algebraically closed. In the second case—i.e. if K is dense in the algebraic closure of (K,
)—we even get
for any number of variables X=(X1,...,Xn).
This work contains parts of the second author's thesis [Ri] written under the supervision of the first author. 相似文献