共查询到20条相似文献,搜索用时 31 毫秒
1.
D. I. Panyushev 《Functional Analysis and Its Applications》2004,38(1):38-44
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
2.
S. Ya. Novikov 《Journal of Mathematical Sciences》2004,120(5):1733-1751
We study operators
(not necessarily linear) defined on a quasi-Bahach space X and taking values in the space of real-valued Lebesgue-measurable functions. Factorization theorems for linear and superlinear operators with values in the space
are proved with the help of the Lorentz sequence spaces
. Sequences of functions belonging to fixed bounded sets in the spaces
are characterized for
and
. The possibility of distinguishing weak type operators (bounded in the space
) from operators factorizable through
is obtained in terms of sequences of independent random variables. A criterion under which an operator is symmetrically bounded in order in
, is established. Some refinements of the above-mentioned results are obtained for translation shift-invariant sets and operators. Bibliography: 30 titles. 相似文献
3.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
4.
A. A. Dosiev 《Functional Analysis and Its Applications》2003,37(1):61-64
This note deals with homological characteristics of algebras of holomorphic functions of noncommuting variables generated by a finite-dimensional nilpotent Lie algebra
. It is proved that the embedding
of the universal enveloping algebra
of
into its Arens–Michael hull
is an absolute localization in the sense of Taylor provided that
相似文献
5.
V. V. Lebedev 《Functional Analysis and Its Applications》2002,36(1):25-29
We consider the algebra
of absolutely convergent Fourier series on the circle
. According to the Beurling–Helson theorem, the condition
, implies that
is trivial:
. We construct a nontrivial diffeomorphism
of
onto itself such that
, where (n) is an arbitrary given sequence with
. By analogy with a conjecture due to Kahane, it is natural to suppose that this rate of growth is the slowest possible. 相似文献
6.
Let {S
n}
n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n
i for which
respectively
We thereby obtain conditions for to be a strong limit point of {S
n} or {S
n
/n}. The first of these properties is shown to be equivalent to
for some sequence a
i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between
and
for an increasing function fand suitable sequences n
i and a
i. These sorts of properties are of interest in sequential analysis. Known conditions for
and
(divergence through the whole sequence n) are also simplified. 相似文献
7.
The space
of kth-order linear differential operators on
is equipped with a natural two-parameter family of structures of Diff(
)-modules. To specify this family, one considers the action of differential operators on tensor densities. We give a classification of these modules. 相似文献
8.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
9.
We prove new pointwise inequalities involving the gradient of a function
, the modulus of continuity
of the gradient
, and a certain maximal function
and show that these inequalities are sharp. A simple particular case corresponding to
and
is the Landau type inequality
, where the constant 8/3 is best possible and
. 相似文献
10.
Let H1(
) be the usual Hardy space on
. We show that the couple (H1(
), L(
) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH1(
) +L(
) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H1(
) to L1(
) and also from L(
) to L(
); (ii) V(Nf)=f, V is similtaneously bounded from L1(
) to H1(
) and from L(
) to L(
) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (Lp(
), BMO (
)) for every 1
相似文献
11.
We prove that the Sobolev embedding operator S
d,k,p :
, where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s
2 . 相似文献
12.
In this article we prove the equivalence between the strong isoperimetric inequality #A #A, for any subset A of countable graph cG, and the inequality
for any function with finite variation on cG and null at infinity, with optimal constant. More generally, we prove the equivalence between the isoperimetric inequality # A cP
-1(1/# A) # A and the inequality ||
||cM |
|var, where cM is a Young function and cP its conjugate, and we also obtain an isoperimetric inequality in
as an application. 相似文献
13.
S. V. Astashkin 《Functional Analysis and Its Applications》2003,37(3):221-224
Using new extrapolation estimates for the
- and
-functionals of couples of limit spaces of the
-scale
, we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces close to
and
, which depend only on the
-norms of a function. 相似文献
14.
P. V. Semenov 《Functional Analysis and Its Applications》2002,36(2):159-161
A fixed-point theorem is proved for a broad class of closed-valued
-contractions with
for any positive t and with
. 相似文献
15.
We prove that the maximal isoperimetric function on a Riemannian manifold of conformally hyperbolic type can be reduced to the linear canonical form P(x) = x by a conformal change of the Riemannian metric. In other words, the isoperimetric inequality
, relating the volume V(D) of a domain D to the area
of its boundary, can be reduced to the form
, known for the Lobachevskii hyperbolic space. 相似文献
16.
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
17.
G. A. Kalyabin 《Functional Analysis and Its Applications》2002,36(2):106-113
We describe the construction of extension operators with minimal possible norm m from the half-line to the entire real line for the spaces
and derive the asymptotic estimate
, where
The proof is based on the investigation of the maximum and minimum eigenvalues and the corresponding eigenvectors of some special matrices related to Vandermonde matrices and their inverses, which can be of interest in themselves. 相似文献
18.
The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of
4 which we call the the affine part
of Knarr's surface. We compute all affinities leaving
invariant. After embedding
4 into PG(4,
) we calculate the uniquely determined projective closure
Kn
of
. Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3,
). In this way we determine all planes carrying 1-dimensional algebraic varieties of
Kn
. We exhibit all automorphic collineations of
Kn
. 相似文献
19.
Let P
k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold
with Euler characteristic
contains a path P
k such that each vertex of this path has, in G, degree
. Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd
, this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to
. 相似文献
20.
Dražen Adamović 《Algebras and Representation Theory》2004,7(4):457-469
Let
be the affine Lie algebra associated to the simple finite-dimensional Lie algebra
. We consider the tensor product of the loop
-module
associated to the irreducible finite-dimensional
-module V() and the irreducible highest weight
-module L
k,. Then L
k, can be viewed as an irreducible module for the vertex operator algebra M
k,0. Let A(L
k,) be the corresponding
-bimodule. We prove that if the
-module
is zero, then the
-module
is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras. 相似文献