共查询到20条相似文献,搜索用时 296 毫秒
1.
An affine pseudo-plane X is a smooth affine surface defined over
which is endowed with an
-fibration such that every fiber is irreducible and only one fiber is a multiple fiber. If there is a hyperbolic
-action on X and X is an
-surface, we shall show that the universal covering
is isomorphic to an affine hypersurface
in the affine 3-space
and X is the quotient of
by the cyclic group
via the action
where
and
It is also shown that a
-homology plane X with
and a nontrivial
-action is an affine pseudo-plane. The automorphism group
is determined in the last section. 相似文献
2.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》1994,1(4):403-436
Let
and let
In this paper we investigate the relation between the frame operator
and the matrix
whose entries
are given by
for
Here
, for any
We show that
is bounded as a mapping of
into
if and only if
is bounded as a mapping of
into
Also we show that
if and
only if
where
denotes the identity operator of
and
respectively, and
Next, when
generates a frame, we have that
has an upper frame bound, and the minimal dual function
can be computed as
The results of this paper extend, generalize, and rigourize results of Wexler and Raz and of Qian, D. Chen, K. Chen, and
Li on the computation of dual functions for finite, discrete-time Gabor expansions to the infinite, continuous-time case.
Furthermore, we present a framework in which one can show that certain smoothness and decay properties of a
generating a frame are inherited by
In particular, we show that
when
generates a frame
Schwartz space). The proofs of the main results of this paper rely heavily on a technique introduced by Tolimieri and Orr
for relating frame bound questions on complementary lattices by means of the Poisson summation formula. 相似文献
3.
In this paper we show that there exists a
-coreset for k-median and k-means clustering of n points in
which is of size independent of n. In particular, we construct a
-coreset of size
for k-median clustering, and of size
for k-means clustering. 相似文献
4.
In this paper we study the worst-case error (of numerical integration) on the unit sphere
for all functions in the unit ball of the Sobolev space
where
More precisely, we consider infinite sequences
of m(n)-point numerical integration rules
where: (i)
is exact for all spherical polynomials of degree
and (ii)
has positive weights or, alternatively to (ii), the sequence
satisfies a certain local regularity property. Then we show that the worst-case error (of numerical integration)
in
has the upper bound
where the constant c depends on s and d (and possibly the sequence
This extends the recent results for the sphere
by K. Hesse and I.H. Sloan to spheres
of arbitrary dimension
by using an alternative representation of the worst-case error. If the sequence
of numerical integration rules satisfies
an order-optimal rate of convergence is achieved. 相似文献
5.
Wolter Groenevelt 《Transformation Groups》2007,12(1):77-116
We introduce an algebra
consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of
Sahi's double affine Hecke algebra related to the affine root system of type
. We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra
, and the corresponding Fourier transforms. These eigenfunctions are nonsymmetric versions of the Wilson polynomials and the
Wilson functions. 相似文献
6.
Lisa Jeffrey Young-Hoon Kiem Frances C. Kirwan Jonathan Woolf 《Transformation Groups》2006,11(3):439-494
This paper studies intersection theory on the compactified moduli space
of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface
of genus
where n and d may have common factors. Because of the presence of singularities we work with the intersection cohomology
groups
defined by Goresky and MacPherson and the ordinary cohomology groups of a certain partial resolution of singularities
of
Based on our earlier work [25], we give a precise formula for the intersection cohomology pairings and provide a method to
calculate pairings on
The case when n = 2 is discussed in detail. Finally Witten's integral is considered for this singular case. 相似文献
7.
The interassociates of the free commutative semigroup on n generators, for n > 1, are identified. For fixed n, let (S, ·)
denote this semigroup. We show that every interassociate can be written in the form
, depending only on a n-tuple
. Next, if
and
are isomorphic interassociates of (S, ·) such that
, for xii and xj in the generating set of S, then
. Moreover,
if and only if
is a permutation of
. 相似文献
8.
We provide a direct computational proof of the known inclusion
where
is the product Hardy space defined for example by R. Fefferman and
is the classical Hardy space used, for example, by E.M. Stein. We
introduce a third space
of Hardy type and analyze the interrelations among these spaces. We give simple sufficient conditions for a given function
of two variables to be the double Fourier transform of a function in
and
respectively. In particular, we obtain a broad class of multipliers on
and
respectively. We also present analogous sufficient conditions in the case of double trigonometric series and, as a by-product,
obtain new multipliers on
and
respectively. 相似文献
9.
Zachary Mesyan 《Semigroup Forum》2007,75(3):648-675
Let
be a countably infinite set,
the group of permutations of
, and
the monoid of self-maps of
. Given two subgroups
, let us write
if there exists a finite subset
such that the groups generated by
and
are equal. Bergman and Shelah showed that the subgroups which are closed in the function topology on S fall into exactly
four equivalence classes with respect to
. Letting
denote the obvious analog of
for submonoids of E, we prove an analogous result for a certain class of submonoids of E, from which the theorem for groups
can be recovered. Along the way, we show that given two subgroups
which are closed in the function topology on S, we have
if and only if
(as submonoids of E), and that
for every subgroup
(where
denotes the closure of G in the function topology in S and
its closure in the function topology in E). 相似文献
10.
Nonlinear Approximation by Trigonometric Sums 总被引:7,自引:0,他引:7
We investigate the
-error of approximation to a function
by a linear combination
of
exponentials
on
where the frequencies
are allowed to depend on
We bound this error in terms of the smoothness and other properties of
and show that our bounds are best possible in the sense of approximation of certain classes of functions. 相似文献
11.
The digitisation
of a real disc
having radius
and centre
consists of all integer points inside
, i.e.,
In this paper we show that there are
different (up to translations) digitisations of discs having radius
. More formally,
The result is of interest in the area of digital image processing because it describes how large the impact of the object
position can be on its digitisation. 相似文献
12.
C. Carton-Lebrun 《Journal of Fourier Analysis and Applications》1995,2(1):49-64
For
define
where
Pointwise estimates and weighted inequalities describing the local Lipschitz continuity
of
are established. Sufficient conditions are found
for the boundedness of
from
into
and a spherical restriction property is proved. A study of the moment subspaces of
is next developed in the one-variable case, for
locally integrable,
a.e. It includes a decomposition theorem and a complete classification of all possible sequences of moment subspaces in
Characterizations are also given for each class. Applications related to the approximation and decomposition of
are discussed. 相似文献
13.
Jan Draisma 《Transformation Groups》2006,11(4):609-624
For a finite-dimensional representation
of a group G, the diagonal action of G on
p-tuples of elements of M, is usually poorly understood. The algorithm presented here computes a geometric characteristic
of this action in the case where G is connected and reductive, and
is a morphism of algebraic groups: The algorithm takes as input the
weight system of M, and it returns the number of irreducible components
of the null-cone of G on
for large p. The paper concludes with a theorem that if the characteristic is zero and G is semisimple, then only few M have
the property that
is small for all p. 相似文献
14.
Let
be a nontrivial probability measure on the unit circle
the density of its absolutely continuous part,
its Verblunsky coefficients, and
its monic orthogonal polynomials. In this paper we compute the coefficients of
in terms of the
. If the function
is in
, we do the same for its Fourier coefficients. As an application we prove that if
and if
is a polynomial, then with
and S the left-shift operator on sequences we have
We also study relative ratio asymptotics of the reversed polynomials
and provide a necessary and sufficient condition in terms of the Verblunsky coefficients of the measures
and
for this difference to converge to zero uniformly on compact subsets of
. 相似文献
15.
Jesus Jeronimo Castro 《Discrete and Computational Geometry》2007,37(3):409-417
Let
be a family of convex figures in the plane. We say that
has property T if there exists a line intersecting every member of
. Also, the family
has property T(k) if every k-membered subfamily of
has property T. Let B be the unit disc centered at the origin. In this paper we prove that if a finite family
of translates of B has property T(4) then the family
, where
, has property T. We also give some results concerning families of translates of the unit disc which has either property T(3)
or property T(5). 相似文献
16.
We show that every function in the Hardy space can be approximated by linear combinations of translates and dilates of a synthesizer
, provided only that
and
satisfies a mild regularity condition. Explicitly, we prove scale averaged approximation for each
,
where
is an arbitrary lacunary sequence (such as
) and the coefficients
are local averages of f. This formula holds in particular if the synthesizer
is in the Schwartz class, or if it has compact support and belongs to
for some
in terms of differences of
. 相似文献
17.
M. Vsemirnov 《Transformation Groups》2006,11(2):295-304
It is proved that for any prime
the group
is a quotient of
相似文献
18.
Regular Semigroups with Inverse Transversals 总被引:2,自引:0,他引:2
Fenglin Zhu 《Semigroup Forum》2006,73(2):207-218
Let C be a semiband with an inverse transversal
. In [7], G.T. Song and F.L. Zhu construct a fundamental regular semigroup
with an inverse transversal
.
is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations,
and the operation-although not the usual composition-is defined by means of composition. Any full regular subsemigroup T of
is a fundamental regular semigroup with inverse transversal
. Moreover, any regular semigroup S with an inverse transversal
is proved to be an idempotent-separating coextension of a full regular subsemigroup T of some
. By means of a full
regular subsemigroup T of some
and by means of an inverse semigroup K satisfying some conditions, in this paper, we construct a regular semigroup
with inverse transversal
such that
is isomorphic to K and
to T. Furthermore, it is proved that if S is a regular semigroup with an inverse transversal
then S can be constructed from the corresponding T and from
in this way. 相似文献
19.
The central result of this paper is a sandwiching theorem for semigroups acting on Banach lattices with order continuous norm.
As a preparation we show that the norm of a Banach lattice
is order continuous if and only if every order bounded weak null sequence in
is a norm null sequence. From the sandwiching result we deduce approximation formulas for the modulus semigroup and its generator.
For example,
if
generates a dominated
-semigroup
we show that
converges to the modulus semigroup
of
as
, and
converges (in the strong resolvent sense) to the generator of the modulus semigroup of
as
. 相似文献
20.
This paper deals with the homogenization of a sequence of non-linear conductivity energies in a bounded open set
The energy density is of the same order as
where
is periodic, u is a vector-valued function in
and
The conductivity
is equal to 1 in the "hard" phases composed by
two by two disjoint-closure periodic sets while
tends uniformly to 0 in the "soft" phases composed by periodic thin layers which separate the hard phases. We prove that
the limit energy, according to γ-convergence, is a multi-phase functional equal to the sum of the homogenized energies (of
order 1) induced by the hard phases plus an interaction energy (of order 0) due to the soft phases. The number of limit phases
is less than or equal to N and is obtained by evaluating the γ-limit of the rescaled energy of density
in the torus. Therefore, the homogenization result is achieved by a double γ-convergence procedure since the cell problem
depends on ε. 相似文献