共查询到20条相似文献,搜索用时 31 毫秒
1.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
2.
J. Ruppenthal 《Mathematische Zeitschrift》2009,263(2):447-472
Let X be a regular irreducible variety in , Y the associated homogeneous variety in , and N the restriction of the universal bundle of to X. In the present paper, we compute the obstructions to solving the -equation in the L
p
-sense on Y for 1 ≤ p ≤ ∞ in terms of cohomology groups . That allows to identify obstructions explicitly if X is specified more precisely, for example if it is equivalent to or an elliptic curve.
相似文献
3.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
4.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
5.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-invariants of Riemannian foliations
Luis Sanguiao 《Annals of Global Analysis and Geometry》2008,33(3):271-292
For a Riemannian foliation on a closed manifold M, we define L
2-spectral sequence Betti numbers and spectral sequence Novikov–Shubin invariants. The spectral sequence of the lift of to the universal covering of M is used in the definitions. These invariants are natural extensions of the L
2-Betti numbers and the Novikov–Shubin invariants of differentiable manifolds. It is shown that these numbers are invariant
by foliated homotopy equivalences, and they are computed for several examples.
相似文献
6.
Jiancheng Liu 《Geometriae Dedicata》2007,129(1):35-45
We prove firstly the classification theorem for p-harmonic morphisms between Euclidean domains. Secondly, we show that if is a p-harmonic morphism (p ≥ 2) from a complete Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive scalar curvature such that the L
q
-energy is finite, then is constant, which improve the corresponding result due to G. Choi, G. Yun in (Geometriae Dedicata 101 (2003), 53–59).
相似文献
7.
Equations with two time scales (refinement equations or dilation equations) are central to wavelet theory. Several applications
also include an inhomogeneous forcing term F(t). We develop here a part of the existence theory for the inhomogeneous refinement
equation
where a (k) is a finite sequence and F is a compactly supported distribution on ℝ.
The existence of compactly supported distributional solutions to an inhomogeneous refinement equation is characterized in
terms of conditions on the pair (a, F).
To have Lp solutions from F ∈ Lp(ℝ), we construct by the cascade algorithm a sequence of functions φ0 ∈ Lp(ℝ) from a compactly supported initial function ℝ as
A necessary and sufficient condition for the sequence {φn} to converge in Lp(ℝ)(1 ≤ p ≤ ∞) is given by the p-norm joint spectral radius of two matrices derived from the mask a. A convexity property
of the p-norm joint spectral radius (1 ≤ p ≤ ∞) is presented.
Finally, the general theory is applied to some examples and multiple refinable functions.
Acknowledgements and Notes. Research supported in part by Research Grants Council and City University of Hong Kong under Grants #9040281, 9030562, 7000741. 相似文献
8.
In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C
2m
-boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L
p
-L
q
-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on
and the Lopatinskii–Shapiro condition on are necessary for these L
p
-L
q
-estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces
of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.
相似文献
9.
Cleon S. Barroso 《Annals of Global Analysis and Geometry》2009,35(3):231-241
We study the behavior of complete graphs in with L
p
-finite r-curvature, that is, whose length of the r-th Newton transformation |P
r
| is in L
p
, for some p ≥ 1. Moreover, we use a monotonicity formulae to establish an L
p
-lower bound for |P
r
| in balls. As application, we prove some new Bernstein-type results.
相似文献
10.
K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex
Song Li 《数学学报(英文版)》1999,15(3):395-406
An inverse theorem for the best weighted polynomial approximation of a function in
(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial
approximation in
, wherew
α is a Jacobi-type weight onS, 0<p ≤ ∞,S is a simplex andW
λ is a Freud weight. For Ditzian-TotikK-functionals onL
p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression. 相似文献
11.
Song Li 《中国科学A辑(英文版)》2003,46(3):364-375
The purpose of this paper is to investigate the refinement equations of the form
where the vector of functions ϕ=(ϕ
1..., ϕ
r
)
T
is in (L
p
(ℝ
s
))
r
, 1⩽p⩽∞, a(α), α∈ℤ
s
is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vector of compactly supported functions φ
0∈(L
p
(ℝ
s
))
r
and use the iteration schemes f
n
:=Q
a
n
φ
0, n=1,2,..., where Q
n
is the linear operator defined on (L
p
(ℝ
s
))
r
given by
This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of some linear operators
determined by the sequence a and the set B restricted to a certain invariant subspace, where the set B is a complete set of representatives of the distinct cosets of the quotient group ℤs/Mℤs containing 0. 相似文献
12.
Shiquan WU 《应用数学学报(英文版)》1996,12(4):377-383
Letn, s
1,s
2, ... ands
n
be positive integers. Assume
is an integer for eachi}. For
,
, and
, denotes
p
(a)={j|1jn,a
j
p},
, and
.
is called anI
t
p
-intersecting family if, for any a,b
,a
i
b
i
=min(a
i
,b
i
)p for at leastt i's.
is called a greedyI
t
P
-intersecting family if
is anI
t
p
-intersecting family andW
p
(A)W
p
(B+A
c
) for anyAS
p
(
) and any
with |B|=t–1.In this paper, we obtain a sharp upper bound of |
| for greedyI
t
p
-intersecting families in
for the case 2ps
i
(1in) ands
1>s
2>...>s
n
.This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China. 相似文献
13.
MUCHUNLAI TANGXIANJIANG 《高校应用数学学报(英文版)》1998,13(1):31-38
In this paper L^p-L^q estimates for the solution u(x,t) to the following perturbed high-er order hyperbolic equation are considered, (ρπ--a△)(ρπ--b△)u V(x)u=O, x∈R^n,n≥6, ρ1eu(x,O) = O, ρ^3eu(x,O) = f(x), (j = O,1,2).We assume that the otential V(x) and the initial data f(x) are compactly supported, andV(x) is sufficiently small, then the solution u (x,t) of the above problem satisfies the same L^p-L^q estimates as that of the unperturbed problem. 相似文献
14.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
15.
In this paper, we obtain that a strongly singular integral operator is bounded on
space for 1 < p < ∞. We also obtain that a strongly singular integral operator is a bounded operator from
to
for some weight w and 0 < p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on
for some w and 0 < p ≤ 1.
Supported by National 973 Program of China (Grant No. 19990751) 相似文献
16.
Consider a right-invariant sub-Laplacian L on an exponential solvable Lie group G, endowed with a left-invariant Haar measure. Depending on the structure of G and possibly also that of L, L may admit differentiable Lp-functional calculi, or may be of holomorphic Lp-type for a given p≠2, as recent studies of specific classes of groups G and sub-Laplacians L have revealed. By “holomorphic Lp-type” we mean that every Lp-spectral multiplier for L is necessarily holomorphic in a complex neighborhood of some point in the L2-spectrum of L. This can only arise if the group algebra L1(G) is non-symmetric. In this article we prove that, for large classes of exponential groups, including all rank one AN-groups, a certain Lie algebraic condition, which characterizes the non-symmetry of L1(G) [37], also suffices for L to be of holomorphic L1-type. Moreover, if this condition, which was first introduced by J. Boidol [6] in a different context, holds for generic points in the dual
* of the Lie algebra of G, then L is of holomorphic Lp-type for every p≠2. Besides the non-symmetry of L1(G), also the closedness of coadjoint orbits plays a crucial role. We also discuss an example of a higher rank AN-group. This example and our results in the rank one case suggest that sub-Laplacians on exponential Lie groups may be of holomorphic L1-type if and only if there exists a closed coadjoint orbit Ω
* such that the points of Ω satisfy Boidol's condition. In the course of the proof of our main results, whose principal strategy is similar as in [8], we develop various tools which may be of independent interest and largely apply to more general Lie groups. Some of them are certainly known as “folklore” results. For instance, we study subelliptic estimates on representation spaces, the relation between spectral multipliers and unitary representations, and develop some “holomorphic” and “continuous” perturbation theory for images of sub-Laplacians under “smoothly varying” families of irreducible unitary representations. 相似文献
17.
Xu Cheng 《Bulletin of the Brazilian Mathematical Society》2000,31(2):225-239
We prove that a complete noncompact oriented strongly stable hypersurfaceM
n
with cmc (constant mean curvature)H in a complete oriented manifoldN
n+1
with bi-Ricci curvature, satisfying
alongM, admits no nontrivialL
2 harmonic 1-forms. This implies ifM
n
(2n4) is a complete noncompact strongly stable hypersurface in hyperbolic spaceH
n+1(–1) with cmc
, there exist no nontrivialL
2 harmonic 1-forms onM. We also classify complete oriented strongly stable surfaces with cmcH in a complete oriented manifoldN
3 with scalar curvature
satisfying
. 相似文献
18.
We prove L
r
estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L
q
for 1q+, where the operator satisfies (|s|)||
p
a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases. 相似文献
19.
Pu Zhang 《数学学报(英文版)》2008,24(8):1387-1400
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,
||μ(f)||LP(ω)≤C|Mf|LP(ω) and ||μb(f)||LP(ω)≤C||ML(log L)^1/r f||LP(ω).
The weighted weak L(log L)^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
||μ(f)||LP(ω)≤C|Mf|LP(ω) and ||μb(f)||LP(ω)≤C||ML(log L)^1/r f||LP(ω).
The weighted weak L(log L)^1/r -type estimate is also established when p=1 and ω∈A1. 相似文献
20.
It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the
product spaces
to the Hardy spacesH
r
, (ℝ
n
) and the weak Hardy spaceH
r,∞ (ℝ
n
. As an application of this result, the L
p
,(ℝ
n
) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.
Project supparted in part by the National Natural Science Foundation of Chind (Grant No. 19131080) of China and Doctoral Programme
Foundation of Institution of Higher Education (Grant No. 98002703) of China. 相似文献