共查询到20条相似文献,搜索用时 15 毫秒
1.
Pedro E. Ferreira 《Annals of the Institute of Statistical Mathematics》1982,34(1):423-431
Summary Let {p(x, θ): θ∈Θ} be a family of densities where θ=(θ1,θ2), being θ1 ∈ Θ1 ak-dimensional parameter of interest, θ2 ∈ Θ2 a nuisance parameter and Θ=Θ1×Θ2. To estimate θ1, vector estimating equations g(x,θ1)=(g1(x,θ1),...,gk(x,θ1))=0 are considered. The standardized form of g(x,θ1) is defined as gs=(Eθ(∂g/∂θ′1))−1g. Then, within the classG
1 of unbiased equations (i.e. satisfying Eθ(g)=0 (θ∈Θ)), an equationg
*=0 is said to be optimum if the covariance matrices ofg
s andg
s
*
are such that
is non-negative definite for allg∈
G
1 and θ∈Θ. Sufficient conditions for optimality are discussed and, in particular, conditions for the optimality of the maximum
conditional likelihood equation are analyzed. Special attention is given to non-regular cases. In addition, measures of the
information about θ1 contained in an estimating equation are presented and a Rao-Blackwell theorem is given.
CIENES 相似文献
2.
Franz Kinzl 《Semigroup Forum》1989,38(1):105-118
Let S be a locally compact semigroup. We study the sequence (λn) of the convolution powers of a probability measure λ on S and their shifts by a probability measure η on S. We shall give
sufficient conditions for lim ‖λn−η*λn‖ = 0 (where ‖.‖ denotes the norm). In particular we consider the case the η is a point measure and we study the subsemigroup
LO(λ) = {x ∈ S : lim ‖λn−δX*λn‖ = 0}. We shall give necessary and sufficient conditions for Lo(λ)=S. In this case we want to treat the problem of the convergence of the sequence (λn). 相似文献
3.
Rainer Wittmann 《Israel Journal of Mathematics》1987,59(1):8-28
LetT be a positive linear contraction inL
p (1≦p<∞), then we show that lim ‖T
pf −T
n+1
f‖
p
≦(1 − ε)21/p
(f∈L
p
+
, ε>0 independent off) implies already limn
n→∞ ‖T
nf −T
n+1
n+1f ‖p
p=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown. 相似文献
4.
John J. Benedetto 《Annali di Matematica Pura ed Applicata》1970,86(1):313-324
Summary We consider pseudo-measures T on totally disconnected sets E as finitely additive set functions whit the usual variation norm
‖ ‖v. If
, m(E)=0, T=f′, f ∈L
1, and ‖T‖v<∞ then T is a measure. For arbitrary locally compact abelian groups we give conditions that T be a measure in terms of the
pseudo-measure norm; this result is known for R/2ΠZ.
Entrata in Redazione il 5 gennaio 1969. 相似文献
5.
Suppose that(T
t
)t>0 is aC
0 semi-group of contractions on a Banach spaceX, such that there exists a vectorx∈X, ‖x‖=1 verifyingJ
−1(Jx)={x}, whereJ is the duality mapping fromX toP(X
*). If |<T
t
x,f>|→1, whent→+∞ for somef∈X
*, ‖f‖≤1 thenx is an eigenvector of the generatorA, associated with a purcly imaginary eigenvalue. Because of Lin's example [L], the hypothesis onx∈X is the best possible.
If the hypothesisJ
−1(Jx)={x} is not verified, we can prove that ifJx is a singleton and ifJ
−1(Jx) is weakly compact, then if |<T
t
x, f>|→1, whent→+∞ for somef∈X
*, ‖f‖≤1, there existsy∈J
−1(Jx) such thaty is an eigenvector of the generatorA, associated with a purely imaginary eigenvalue. We give also a counter-example in the case whereX is one of the spaces ℓ1 orL
1. 相似文献
6.
K. M. D'yakonov 《Journal of Mathematical Sciences》1996,78(2):131-141
Let ϕ be a unimodular function on the unit circle
and let Kp(ϕ) denote the kernel of the Toeplitz operator Tϕ in the Hardy space Hp, p≥1;
. Suppose Kp(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in
Kp(ϕ). One of the main results is as follows.
Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q−1=p−1+r−1. Suppose |ϕ|≡1 on
and ϕ∈W
r
1
(i.e.,
). Then Kp(ϕ)⊂W
q
1
. Moreover, for any f∈Kp(ϕ) we have ‖f′‖q≤c(p, r)‖ϕ′‖r ‖f‖. Bibliography: 19 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21.
Translated by K. M. D'yakonov. 相似文献
7.
Bao Yongguang 《分析论及其应用》1995,11(4):15-23
Let ξn −1 < ξn −2 < ξn − 2 < ... < ξ1 be the zeros of the the (n−1)-th Legendre polynomial Pn−1(x) and −1=xn<xn−1<...<x1=1, the zeros of the polynomial
. By the theory of the inverse Pal-Type interpolation, for a function f(x)∈C
[−1,1]
1
, there exists a unique polynomial Rn(x) of degree 2n−2 (if n is even) satisfying conditions Rn(f, ξk) = f (εk) (1 ⩽ k ⩽ n −1); R1
n(f,xk)=f1(xk)(1≤k≤n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation
polynomial {Rn(f, x)} (n is even) and the main result of this paper is that if f∈C
[1,1]
r
, r≥2, n≥r+2, and n is even then |R1
n(f,x)−f1(x)|=0(1)|Wn(x)|h(x)·n3−r·E2n−r−3(f(r)) holds uniformly for all x∈[−1,1], where
. 相似文献
8.
P. Sablonniere 《分析论及其应用》1992,8(3):62-76
Suppose that we want to approximate f∈C[0,1] by polynomials inP, using only its values on Xn={i/n, 0≤i≤n}. This can be done by the Lagrange interpolant Ln f or the classical Bernstein polynomial Bn f. But, when n tends to infinity, Ln f does not converge to f in general and the convergence of Bn f to f is very slow. We define a family of operators B
n
(k)
, n≥k, which are intermediate ones between B
n
(0)
=B
n
(1)
=Bn and B
n
(n)
=Ln, and we study some of their properties. In particular, we prove a Voronovskaja-type theorem which asserts that B
n
(k)
f−f=O(n−[(k+2)/2]) for f sufficiently regular.
Moreover, B
n
(k)
f uses only values of Bn f and its derivaties and can be computed by De Casteljau or subdivision algorithms. 相似文献
9.
Small into-isomorphism from L∞(A,μ) into L∞(B,υ) 总被引:1,自引:0,他引:1
DING Guanggui 《中国科学A辑(英文版)》2001,44(3):273-279
In this paper we shall assert that if T is an isomorphism of L∞(Ω1, A, μ) into L∞(Ω2, B, υ) satisfying the condition ‖T‖·‖T
−1‖⩽1+ɛ for ɛ∈
, then
is close to an isometry with an error less than 6ε in some conditions. 相似文献
10.
We generalize a result by H. Brezis, Y. Y. Li and I. Shafrir [6] and obtain an Harnack type inequality for solutions of −Δu = |x|2α Ve u in Ω for Ω ⊂ ℝ2 open, α ∈ (−1, 0) and V any Lipschitz continuous function satisfying 0 < a ≤ V ≤ b < ∞ and ‖∇V‖∞ ≤ A. 相似文献
11.
E. G. Goluzina 《Journal of Mathematical Sciences》1998,89(1):958-966
Let TR be the class of functions
that are regular and typically real in the disk E={z:⋱z⋱<1}. For this class, the region of values of the system {f(z0), f(r)} for z0 ∈ ℝ, r∈(-1,1) is studied. The sets Dr={f(z0):f∈TR, f(r)=a} for −1≤r≤1 and Δr={(c2, c3): f ∈ TR, −f(−r)=a} for 0<r≤1 are found, where aε(r(1+r)−2, r(1−r)−2) is an arbitrary fixed number. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 69–79. 相似文献
12.
Z. Ditzian 《Israel Journal of Mathematics》1985,52(4):341-354
Equivalences between the condition |P
n
(k)
(x)|≦K(n
−1√1−x
2+1/n
2)
k
n
-a, whereP
n(x) is the bestn-th degree polynomial approximation tof(x), and the Peetre interpolation space betweenC[−1,1] and the space (1−x
2)
k
f
(2k)(x)∈C[−1,1] is established. A similar result is shown forE
n(f)=
‖f−P
n‖
C[−1,1]. Rates other thann
-a are also discussed.
Supported by NSERC grant A4816 of Canada. 相似文献
13.
Alain Haraux 《Journal d'Analyse Mathématique》2005,95(1):297-321
IfA=A
*≥0 on the real Hilbert spaceH=L
2
(Ω, dμ) withKerA=A
−1
({0})∈0, (I+A)−1 compact andf(u)=c|u|
p−1
u withc>0,p>1, the solutions ofu”+u’+Au+f(u)=0 tend to 0 in norm at least liket
−1/(p−1)
ast→∞. Here it is shown that the set of initial data of those solutions tending to 0 exponentially fast has near 0 the structure
of a manifold with codimension dim(Ker A). If, in addition,A=−Δ with Neumann homogeneous boundary conditions, we show that the following alternative holds true: eitheru(t) tends to 0 exponentially fast, or ‖u(t)‖≥γt
−1/(p−1) with γ>0 fort≥1. 相似文献
14.
S Ponnusamy 《Proceedings Mathematical Sciences》1994,104(2):397-411
Denote byS
* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a
2z2+...+anzn+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very
simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)μ−1<h(z) implies f∈S*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results
considerably extend the earlier works of Miller and Mocanu [6] and others. 相似文献
15.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
16.
W.M. Priestly 《Semigroup Forum》1998,56(3):301-322
t , for t ≥ 0, be a strongly continuous Markovian semigroup acting on C(X), where X is a compact Hausdorf space, and let D
denote the domain of its infinitesimal generator Z. Suppose D contains a (perhaps finite) family of functions f separating
the points of X and satisfying Zf2 = 2fZf. If either
(1) there exists δ > 0 such that (Tt f)2∈ D if 0 ≤ t ≤δ for each f in this family; or
(1′) for some core D′ of Z, g ∈ D′ implies g2∈ D, then the underlying Markoff process on X is deterministic. That is, there exists a semiflow — a semigroup (under composition)
of continuous functions φt from X into X — such that Ttf(x) = f(φt (x)). If the domain D should be an algebra then conditions (1) and (1′) hold trivially. Conversely, if we have a separating
family satisfying Zf2 = 2fZf then each of these conditions implies that D is an algebra. It is an open question as to whether these conditions
are redundant. If the functions φt are homeomorphisms from X onto X, then of course we have a Markovian group induced by a flow. This result is obtained by
first providing general results about the null-space N of the (function-valued) positive semidefinite quadratic form defined
by < f, g > = Z(fg) - fZg - gZf. The set N can be defined for any generator Z of a strongly continuous Markovian semigroup
and is equivalently given by
N = {f ∈ D| f2∈ D and Zf2 = 2fZf}
= {f ∈ D| Tt(f2)-(Ttf)2 is o(t2) in C(X)}.
In the general case N is an algebra closed under composition with any C1-function φ from the reals to the reals, and Z(φ[f]) = (Zf)φ′[f] if f ∈ N. This "chain rule" on N (on which Z must act as
a derivation) is a special case of a theorem for C2-functions φ which holds more generally for all f in d, viz.,
Z(φ[f] = (Zf) φ′[f] + ? <f, f> φ″[f],
Provided Z is a local operator and D is an algebra. In this case the form < f, g > itself enjoys the relation
< φ[f], ψ[g] > = φ′ [f] ψ′[g] < f, g >,
for C2functions φ and ψ. Some of the results and their proofs continue to hold when the setting is switched from the commutative
C*-algebra C(X) to a general (noncommutative) C*-algebra A. In the norm continuous case we obtain a sharp characterization
of Markovian semigroups that are groups: Let Tt = etz , defined for t ≥ 0, be a Markovian semigroup acting on a C*-algebra A that is norm continuous, i.e., ||Tt - I|| ⇒ 0 as t ⇒ 0 +. Assume Z(a2) = a(Za) + (Za) a for some (perhaps finite) set of self-adjoint elements a that generate a Jordan algebra dense among the
self-adjoint elements of A. The etz , -∞ < t < ∞, is a group of Markovian operators. 相似文献
17.
We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then there is, a best L1-approximant to f by functions which are n-convex on (0,1). We then show that if f∈L∞[0,1], then any best Lp-approximant, fp, to f by n-convex, functions is bounded and hence, f has the Pólya-one property, i.e., fp converges a.e. as p decreases to one. 相似文献
18.
V. M. Badkov 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):64-77
Two-sided pointwise estimates are established for polynomials that are orthogonal on the circle |z| = 1 with respect to the weight ϕ(τ): = h(τ)|sin(τ/2)|−1
g(|sin(τ/2)|) (τ ∈ ℝ), where g(t) is a concave modulus of continuity slowly changing at zero such that t
−1
g(t) ∈ L
1[0, 1] and h(τ) is a positive function from the class C
2π
with a modulus of continuity satisfying the integral Dini condition. The obtained estimates are applied to find the order
of the distance from the point t = 1 to the greatest zero of a polynomial orthogonal on the segment [−1, 1]. 相似文献
19.
E. Ballico 《Annali dell'Universita di Ferrara》1999,45(1):123-125
Fix integersg, k andt witht>0,k≥3 andtk<g/2−1. LetX be a generalk-gonal curve of genusg andR∈Pic
k
(X) the uniqueg
k
1
onX. SetL:=K
X⊗(R
*)⊗t.L is very ample. Leth
L:X→P(H
0(X, L)*) be the associated embedding. Here we prove thath
L(X) is projectively normal. Ifk≥4 andtk<g/2−2 the curveh
L(X) is scheme-theoretically cut out by quadrics.
The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献