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1.
Pu Zhang 《Journal of Algebra》2002,250(2):709
Generalized Green classes are introduced; some basic properties of members in a generalized Green class are studied. Finally, we apply the results to
(Λ), the Ringel–Hall algebra of a finite-dimensional hereditary algebra Λ over a finite field. In particular, it is proved that
(Λ) belongs to a suitable generalized Green class, and that there is direct decomposition of spaces
(Λ) =
(Λ) J, where
(Λ) is the composition algebra of Λ and J is a twisted Hopf ideal of
(Λ), which is exactly the orthogonal complement of
(Λ). 相似文献
2.
Let Ω be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on Ω that we call B-kernels. When Ω is the open unit disk
and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space
(k) shares certain properties with the classical Bergman space L2α of the unit disk. For example, the weighted Bergman kernels kβw(z)=(1−wz)−β, 1β2 are Bergman-type kernels. Furthermore, for any Bergman-type kernel k one has H2
(k)L2a, where the inclusion maps are contractive, and Mζ, the operator of multiplication with the identity function ζ, defines a contraction operator on
(k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace
of
(k) is a Bergman-type kernel as well. For the weighted Bergman kernels kβ this result even holds for all
ζ-invariant subspace
of index 1, i.e., whenever the dimension of
/ζ
is one. Second, if
is any multiplier invariant subspace of
(k), and if we set
*=
z
, then Mζ
is unitarily equivalent to Mζ acting on a space of
*-valued analytic functions with an operator-valued reproducing kernel of the type
where V is a contractive analytic function V :
→
(
,
*), for some auxiliary Hilbert space
. Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of
(kβ), 1β2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner–outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs. 相似文献
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3.
In 1929, Birkhoff proved the existence of an entire function F on
with the property that for any entire function f there exists a sequence {ak} of complex numbers such that {F(ζ+ak)} converges to f (ζ) uniformly on compact sets. Luh proved a variant of Birkhoff's theorem and the second author proved a theorem analogous to that of Luh for the multiplicative group
*. In this paper extensions of the above results to the multi-dimensional case are proved. Let M(n,
) be the set of all square matrices of degree n with complex coefficients, and let G=GL(n,
) be the general linear group of degree n over
. We denote by
(G) the set of all holomorphic functions on G. Similarly, we define
(
). Let K be the
(G)-hull of a compact set K in G. Finally we denote by B(G) the set of all compact subsets K of G with K=K such that there exists a holomorphic function f on M(n,
) with f(0)(f(K)), where (f(K)) is the
(
)-hull of f(K). Our main result is the following. There exists a holomorphic function F on G such that for any KB(G), for any function f holomorphic in some neighbourhood of K, and for any >0, there exists CG with maxZK |F(CZ)−f(Z)|<. 相似文献
4.
S. V. Khrushchev 《Journal of Approximation Theory》2002,116(2):268-342
The set
of all probability measures σ on the unit circle
splits into three disjoint subsets depending on properties of the derived set of {|n|2dσ}n0, denoted by Lim(σ). Here {n}n0 are orthogonal polynomials in L2(dσ). The first subset is the set of Rakhmanov measures, i.e., of σ
with {m}=Lim(σ), m being the normalized (m(
)=1) Lebesgue measure on
. The second subset Mar(
) consists of Markoff measures, i.e., of σ
with mLim(σ), and is in fact the subject of study for the present paper. A measure σ, belongs to Mar(
) iff there are >0 and l>0 such that sup{|an+j|:0jl}>, n=0,1,2,…,{an} is the Geronimus parameters (=reflectioncoefficients) of σ. We use this equivalence to describe the asymptotic behavior of the zeros of the corresponding orthogonal polynomials (see Theorem G). The third subset consists of σ
with {m}Lim(σ). We show that σ is ratio asymptotic iff either σ is a Rakhmanov measure or σ satisfies the López condition (which implies σMar(
)). Measures σ satisfying Lim(σ)={ν} (i.e., weakly asymptotic measures) are also classified. Either ν is the sum of equal point masses placed at the roots of zn=λ, λ
, n=1,2,…, or ν is the equilibrium measure (with respect to the logarithmic kernel) for the inverse image under an m-preserving endomorphism z→zn, n=1,2,…, of a closed arc J (including J=
) with removed open concentric arc J0 (including J0=). Next, weakly asymptotic measures are completely described in terms of their Geronimus parameters. Finally, we obtain explicit formulae for the parameters of the equilibrium measures ν and show that these measures satisfy {ν}=Lim(ν). 相似文献
5.
Ding-Xuan Zhou 《Applied and Computational Harmonic Analysis》2001,11(3):142
Let a:=(a(α))α
s be a finitely supported sequence of r×r matrices and M be a dilation matrix. The subdivision sequence {(an(α))α
s:n
} is defined by a1=a and
Let 1≤p≤∞ and f=(f1,…,fr)T be a vector of compactly supported functions in Lp(
s). The stability is not assumed for f. The purpose of this paper is to give a formula for the asymptotic behavior of the Lp-norms of the combinations of the shifts of f with the subdivision sequence coefficients:
Such an asymptotic behavior plays an essential role in the investigation of wavelets and subdivision schemes. In this paper we show some applications in the convergence of cascade algorithms, construction of inhomogeneous multiresolution analyzes, and smoothness analysis of refinable functions. Some examples are provided to illustrate the method. 相似文献
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6.
Let f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and (x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping
is injective, that is, for
,
G(f(x),Z/(2e)),
=
if and only if Φ(
)=Φ(
), i.e., (
0,…,
e−1)=(
0,…,
e−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings. 相似文献
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7.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
8.
The aim of the present paper is to develop a theory of best approximation by elements of so-called normal sets and their complements—conormal sets—in the non-negative orthant
I+ of a finite-dimensional coordinate space
I endowed with the max-norm. A normal (respectively, conormal) set arises as the set of all solutions of a system of inequalities fα(x)0 (αA), x
I+ (respectively, fα(x)0 (αA), x
I+), where fα is an increasing function and A is an arbitrary set of indices. We consider these sets as analogues (in a certain sense) of convex sets, and we use the so-called min-type functions as analogues of linear functions. We show that many results on best approximation by convex and reverse convex sets and corresponding separation theory (but not all of them) have analogues in the case under consideration. At the same time there are no convex analogues for many results related to best approximation by normal sets. 相似文献
9.
The following reaction-diffusion system in spatially non-homogeneous almost-periodic media is considered in a bounded domain
: (1) ∂tu=Au−f(u)+g, u|∂Ω=0. Here u=(u1,…,uk) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A has the following structure: where aijl(y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f(u), the longtime behavior of solutions of (1) can be described in terms of the global attractor
of the associated dynamical system and that the attractors
, 0<<01, converge to the attractor
of the homogenized problem (1) as →0. Moreover, in the particular case of periodic media, we give explicit estimates for the distance between the non-homogenized
and the homogenized
attractors in terms of the parameter . 相似文献
10.
Let
be an algebraic algebra over an infinite field K and let
(
) be its group of units. We prove a stronger version of Hartley's conjecture for
, namely, if a Laurent polynomial identity (LPI, for short) f = 0 is satisfied in
(
), then
satisfies a polynomial identity (PI). We also show that if
is non-commutative, then
is a PI-ring, provided f = 0 is satisfied by the non-central units of
. In particular,
is locally finite and, thus, the Kurosh problem has a positive answer for K-algebras whose unit group is LPI. Moreover, f = 0 holds in
(
) if and only if the same identity is satisfied in
. The last fact remains true for generalized Laurent polynomial identities, provided that
is locally finite. 相似文献
11.
Larry Smith 《Finite Fields and Their Applications》2002,8(4):504
Let
q be the finite field with q elements, q=pν, p
a prime, and Mat2.2(
q) the vector space of 2×2-matrices over
. The group GL(2,
) acts on Mat2,2(
q) by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where the trace and determinant generate the ring of invariants, several new invariants appear in the case of finite fields. 相似文献
12.
A. Bir 《Indagationes Mathematicae》2000,11(4):499
Let z1, z2, …, zn be complex numbers, and write
for their power sums. Let
where the minimum is taken under the condition that
. In this paper we prove that
. 相似文献
13.
Leonid Golinskii 《Journal of Approximation Theory》2002,118(2):257-274
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg
recurrences. We assume that the reflection coefficients tend to some complex number a with 0<a<1. The orthogonality measure μ then lives essentially on the arc {eit :αt2π−α} where sin
with α(0,π). Under the certain rate of convergence it was proved in (Golinskii et al. (J. Approx. Theory96 (1999), 1–32)) that μ has no mass points inside this arc. We show that this result is sharp in a sense. We also examine the case of the whole unit circle and some examples of singular continuous measures given by their reflection coefficients. 相似文献
14.
Chen Xiaoman Cao Guangfu Guo Kunyu 《Journal of Mathematical Analysis and Applications》2000,250(2):1666
The present paper shows that the algebra
generated by {C| Aut(Bn)} is cyclic on H2(Bn), and any nonconstant function f H2(Bn) is a cyclic vector of
. In addition, the hypercyclic and cyclic composition operators will be discussed. 相似文献
15.
Nicholas Hanges 《Journal of Functional Analysis》2004,210(2):295-320
We study a partial differential operator
with analytic coefficients, which is of the form “sum of squares”.
is hypoelliptic on any open subset of
, yet possesses the following properties: (1)
is not analytic hypoelliptic on any open subset of
that contains 0. (2) If u is any distribution defined near
with the property that
is analytic near 0, then u must be analytic near 0. (3) The point 0 lies on the projection of an infinite number of Treves curves (bicharacteristics).These results are consistent with the Treves conjectures. However, it follows that the analog of Treves conjecture, in the sense of germs, is false.As far as we know,
is the first example of a “sum of squares” operator which is not analytic hypoelliptic in the usual sense, yet is analytic hypoelliptic in the sense of germs. 相似文献
16.
For fLp(
n), with 1p<∞, >0 and x
n we denote by T(f)(x) the set of every best constant approximant to f in the ball B(x, ). In this paper we extend the operators Tp to the space Lp−1(
n)+L∞(
n), where L0 is the set of every measurable functions finite almost everywhere. Moreover we consider the maximal operators associated to the operators Tp and we prove maximal inequalities for them. As a consequence of these inequalities we obtain a generalization of Lebesgue's Differentiation Theorem. 相似文献
17.
Julien Bichon 《Journal of Algebra》2000,230(2):83
Let
be a (small) category and let F:
→
algf be a functor, where
algf is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra Aaut(F) such that F factorizes through a functor
:
→
coalgf(Aaut(F)), where
coalgf(Aaut(F)) is the category of finite-dimensional measured Aaut(F)-comodule algebras. This general reconstruction result allows us to recapture a finite-dimensional Hopf algebra A from the category
coalgf(A) and the forgetful functor ω:
coalgf(A) →
algf: we have A Aaut(ω). Our universal construction is also done in a C*-algebra framework, and we get compact quantum groups in the sense of Woronowicz. 相似文献
18.
We present sharp bounds on the Kolmogorov probabilistic (N,δ)-width and p-average N-width of multivariate Sobolev space with mixed derivative
, equipped with a Gaussian measure μ in
, that is where 1<q<∞,0<p<∞, and ρ>1 is depending only on the eigenvalues of the correlation operator of the measure μ (see (4)). 相似文献
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19.
G. A. Soifer 《Journal of Algebra》2002,250(2):647
Let
n be a Euclidean space and let S be a Euclidean semigroup, i.e., a subsemigroup of the group of isometries of
n. We say that a semigroup S acts discontinuously on
n if the subset {s S:sK ∩ K ≠ } is finite for any compact set K of
n. The main results of this work areTheorem.If S is a Euclidean semigroup which acts discontinuously on
n, then the connected component of the closure of the linear part ℓ(S) of S is a reducible group.Corollary.Let S be a Euclidean semigroup acting discontinuously on
n; then the linear part ℓ(S) of S is not dense in the orthogonal group O(n).These results are the first step in the proof of the followingMargulis' Conjecture.If S is a crystallographic Euclidean semigroup, then S is a group. 相似文献
20.
Maxim Nazarov 《European Journal of Combinatorics》2004,25(8):1345-1376
Let
be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q. We will regard
as an associative algebra over the field
. Consider the
-module W induced from the tensor product of the evaluation modules over the algebras
and
. The module W depends on two partitions λ of l and μ of m, and on two non-zero elements of the field
. There is a canonical operator J acting on W; it corresponds to the trigonometric R-matrix. The algebra
contains the finite dimensional Hecke algebra Hl+m as a subalgebra, and the operator J commutes with the action of this subalgebra on W. Under this action, W decomposes into irreducible subspaces according to the Littlewood–Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular, we give a formula for the ratio of two eigenvalues of J, corresponding to the “highest” and the “lowest” components. As an application, we derive the well known q-analogue of the hook-length formula for the number of standard tableaux of shape λ. 相似文献