共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Kernel and Trace Operators for Extensions of Brandt Semigroups 总被引:1,自引:0,他引:1
Mario Petrich 《Semigroup Forum》2007,75(1):18-44
Let S be an (ideal) extension of a Brandt semigroup S0 by a Brandt semigroup S1 and let
denote the congruence lattice of S. For
denote by
and
the least and the greatest congruences on S with the same kernel as
respectively, and let
and
have the analogous meaning relative to trace. We establish necessary and sufficient conditions on S in order that one or
more of the operators
be
- or
-homomorphisms on
The conditions are expressed directly in terms of a construction of an extension of S0 and S1 and the proofs make use of a construction of congruences on S expressed by means of congruences on S0 and S1. 相似文献
3.
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
4.
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
5.
6.
On the basis of join-continuous semigroups
, this paper demonstrates among other things that on every complete ortholattice there exists an L-valued topology such that
order convergence is L-topological (this is not always the case with respect to ordinary topologies). Further, the concept
of lower semicontinuous lattice-valued maps permits an extension of the omega-functor
to the general setting of L-valued topological spaces where the importance of
lies in the replacement of ordinary topologies by L-valued topologies. It is shown that
has a right adjoint functor iff the underlying lattice
is continuous. 相似文献
7.
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
8.
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
9.
Arthur D. Grainger 《Semigroup Forum》2006,73(2):234-242
Let J be an infinite set and let
, i.e., I is the collection of all non empty finite subsets of
J. Let
denote the collection of all ultrafilters on the set I and let
be the compact (Hausdorff) right topological semigroup that is the Stone-Cech Compactification of the semigroup
equipped with the discrete topology. This paper continues the study of
that was started in [3] and [5]. In [5], Koppelberg established that
(where K( S) is the smallest ideal of a semigroup S) and for non empty
she established
. In this note, we show that for
such that
is infinite,
is a proper subset of
and
, where
. 相似文献
10.
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
11.
We continue the investigation of some problems in learning theory in the setting formulated by F. Cucker and S. Smale. The
goal is to find an estimator
on the base of given data
that approximates well the regression function
of an unknown Borel probability measure
defined on
We assume that
belongs to a function class
It is known from previous works that the behavior of the entropy numbers
of
in the uniform norm
plays an important role in the above problem. The standard way of measuring the error between a target function
and an estimator
is to use the
norm (
is the marginal probability measure on X generated by
). This method has been used in previous papers. We continue to use this method in this paper. The use of the
norm in measuring the error has motivated us to study the case when we make an assumption on the entropy numbers
of
in the
norm. This is the main new ingredient of thispaper. We construct good estimators in different settings: (1) we know both
and
; (2) we know
but we do not know
and (3) we only know that
is from a known collection of classes but we do not know
An estimator from the third setting is called a universal estimator. 相似文献
12.
Miodrag Zivkovic 《Semigroup Forum》2006,73(3):404-426
Let
be the set of all
Boolean matrices. Let R(A) denote the row space of
, let
, and let
. By extensive computation we found that
and therefore
. Furthermore,
for
. We proved that if
, then the set
contains at least
elements. 相似文献
13.
Mario Petrich 《Semigroup Forum》2007,75(1):45-69
A normal cryptogroup S is a completely regular semigroup in which
is a congruence and
is a normal band. We represent S as a strong semilattice of completely simple semigroups, and may set
For each
we set
and represent
by means of an h-quintuple
These parameters are used to characterize certain quasivarieties of normal cryptogroups. Specifically, we construct the lattice
of quasivarieties generated by the (quasi)varieties
and
This is the lattice generated by the lattice of quasivarieties of normal bands, groups and completely simple semigroups.
We also determine the B-relation on the lattice of all quasivarieties of normal cryptogroups. Each quasivariety studied is
characterized in several ways. 相似文献
14.
Mohan S. Putcha 《Semigroup Forum》2007,75(3):543-553
Let M be a finite monoid with unit group G. By the work of Munn and Ponizovski, the irreducible complex representations of
M are classified according to which J-class (apex) they come from. Consider the irreducible representations of M with apex
. These representations restrict to representations of G, whose components we view as coming from J-classes below G. The remaining
irreducible representations (and their characters) of G are called cuspidal. We show that an irreducible character
of G is cuspidal if and only if
for all idempotents
, where
. 相似文献
15.
A. Askari Hemmat Jean-Pierre Gabardo 《Journal of Fourier Analysis and Applications》2007,13(5):589-606
Given an invertible
matrix B and
a finite or countable subset of
, we consider the collection
generating the closed subspace
of
. If that collection forms a frame for
, one can introduce two different types of shift-generated (SG) dual frames for X, called type I and type II SG-duals, respectively.
The main distinction between them is that a SG-dual of type I is required to be contained in the space
generated by the original frame while, for a type II SG-dual, one imposes that the range of the frame transform associated
with the dual be contained in the range of the frame transform associated with the original frame. We characterize the uniqueness
of both types of duals using the Gramian and dual Gramian operators which were introduced in an article by Ron and Shen and
are known to play an important role in the theory of shift-invariant spaces. 相似文献
16.
David Walnut 《Journal of Fourier Analysis and Applications》1995,2(5):435-452
It is shown that a function
is completely determined by the samples of
on sets
where
and
is irrational if
and of
If
then the samples of
on
and only the first k derivatives of
at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions
and
are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero
and
satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials
that are not Riesz bases for
A signal processing application in which such sampling sets arise naturally is described in detail. 相似文献
17.
Let S be an eventually regular semigroup and
. A weak inverse of a is an element
be such that x = xax. Denote by W(a) the set of all weak inverses of a. Define a relation on
. Then
is the maximum idempotent-separating congruence on S. Analogous characterization of the maximum idempotent-separating congruence
on an eventually orthodox semigroup is given. As important consequences, some sufficient conditions for an eventually regular
subsemigroup T of S to satisfy
are obtained, whence if S is fundamental, then so is T. 相似文献
18.
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
19.
Pedro J. Miana 《Semigroup Forum》2006,73(1):61-74
In this paper new equalities between two different convolution products in cancellative naturally ordered semigroups (but
not in groups) are given. We also give several applications in particular cases
and
相似文献
20.
We give conditions on radial nonnegative weights $W_1We give conditions on radial nonnegative weights
and
on
, for which the a priori inequality
holds with constant independent of
. Here
is the Laplace-Beltrami operator on the sphere
. Due to the relation between
and the tangential component of the gradient,
, we obtain some "Morawetz-type" estimates for
on
. As a consequence we establish some new estimates for the free Schr?dinger propagator
, which may be viewed as certain refinements of the
-(super)smoothness estimates of Kato and Yajima. These results, in turn, lead to the well-posedness of the initial value problem
for certain time dependent first order spherical perturbations of the
dimensional Schr?dinger equation. 相似文献