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1.
We consider the embeddings of certain Besov and Triebel–Lizorkin spaces in spaces of Lipschitz type. The prototype of such embeddings arises from the result of H. Brézis and S. Wainger (1980, Comm. Partial Differential Equations5, 773–789) about the “almost” Lipschitz continuity of elements of the Sobolev spaces H1+n/pp(
n) when 1<p<∞. Two-sided estimates are obtained for the entropy and approximation numbers of a variety of related embeddings. The results are applied to give bounds for the eigenvalues of certain pseudo-differential operators and to provide information about the mapping properties of these operators. 相似文献
2.
Letμbe a Gaussian measure (say, onRn) and letK,LRnbe such thatKis convex,Lis a “layer” (i.e.,L={x: ax, ub} for somea, bRanduRn), and the centers of mass (with respect toμ) ofKandLcoincide. Thenμ(K∩L)μ(K)·μ(L). This is motivated by the well-known “positive correlation conjecture” for symmetric sets and a related inequality of Sidak concerning confidence regions for means of multivariate normal distributions. The proof uses the estimateΦ(x)> 1−((8/π)1/2/(3x+(x2+8)1/2))e−x2/2,x>−1, for the (standard) Gaussian cumulative distribution function, which is sharper than the classical inequality of Komatsu. 相似文献
3.
John R. Collins 《Journal of multivariate analysis》1982,12(4):480-492
Let X1,…,Xn be i.i.d. random vectors in Rm, let θεRm be an unknown location parameter, and assume that the restriction of the distribution of X1−θ to a sphere of radius d belongs to a specified neighborhood
of distributions spherically symmetric about 0. Under regularity conditions on
and d, the parameter θ in this model is identifiable, and consistent M-estimators of θ (i.e., solutions of Σi=1nψ(|Xi−
|)(Xi−
)=0) are obtained by using “re-descenders,” i.e., ψ's wh satisfy ψ(x)=0 for x≥c. An iterative method for solving for
is shown to produce consistent and asymptotically normal estimates of θ under all distributions in
. The following asymptotic robustness problem is considered: finding the ψ which is best among the re-descenders according to Huber's minimax variance criterion. 相似文献
4.
For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K i (A, ?/m) = K i (R, ?/m) for any m relatively prime to the rank and i ≥ 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group. 相似文献
5.
If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ−TμT is bounded on Bpσ,q(Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. 相似文献
6.
Mitsugu Hirasaka 《Journal of Algebra》2001,240(2):1907
Let (X, R) be an association scheme in the sense of P.-H. Zieschang (1996, “An Algebraic Approach to Association Schemes,” Lecture Notes in Mathematics, Vol. 1628, Springer, New York/Berlin), where X is a finite set and R is a partition of X × X. We say that (X, R) is quasi-thin if each element of R has a valency of at most two. In this paper we focus on quasi-thin association schemes with an odd number of points and obtain that (X, R) has a regular automorphism group when nOθ(R) is square-free. 相似文献
7.
We show that for a field k of characteristic p, H
i
(k,ℤ(n)) is uniquely p-divisible for i≠n (we use higher Chow groups as our definition of motivic cohomology). This implies that the natural map K
n
M
(k)?K
n
(k) from Milnor K-theory to Quillen K-theory is an isomorphism up to uniquely p-divisible groups, and that K
n
M
(k) and K
n
(k) are p-torsion free. As a consequence, one can calculate the K-theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de Rham Witt sheaves, for example K
n
(X,ℤ/p
r
)=0 for n>dimX. Another consequence is Gersten’s conjecture with finite coefficients for smooth varieties over discrete valuation rings
with residue characteristic p. As the last consequence, Bloch’s cycle complexes localized at p satisfy all Beilinson-Lichtenbaum-Milne axioms for motivic complexes, except possibly the vanishing conjecture.
Oblatum 21-I-1998 & 26-VII-1999 / Published online: 18 October 1999 相似文献
8.
In 1957, N.G. de Bruijn showed that the symmetric group Sym(Ω) on an infinite set Ω contains a free subgroup on 2card(Ω) generators, and proved a more general statement, a sample consequence of which is that for any group A of cardinality card(Ω), the group Sym(Ω) contains a coproduct of 2card(Ω) copies of A, not only in the variety of all groups, but in any variety of groups to which A belongs. His key lemma is here generalized to an arbitrary variety of algebras V, and formulated as a statement about functors Set V. From this one easily obtains analogs of the results stated above with “group” and Sym(Ω) replaced by “monoid” and the monoid Self(Ω) of endomaps of Ω, by “associative K-algebra” and the K-algebra EndK (V) of endomorphisms of a K-vector-space V with basis Ω, and by “lattice” and the lattice Equiv(Ω) of equivalence relations on Ω. It is also shown, extending another result from de Bruijn's 1957 paper, that each of Sym(Ω), Self(Ω) and EndK(V) contains a coproduct of 2card(Ω) copies of itself.That paper also gave an example of a group of cardinality 2card(Ω) that was not embeddable in Sym(Ω), and R. McKenzie subsequently established a large class of such examples. Those results are shown here to be instances of a general property of the lattice of solution sets in Sym(Ω) of sets of equations with constants in Sym(Ω). Again, similar results - this time of varying strengths - are obtained for Self(Ω), EndK(V), and Equiv(Ω), and also for the monoid Rel(Ω) of binary relations on Ω.Many open questions and areas for further investigation are noted. 相似文献
9.
R 《Journal of Approximation Theory》1993,74(3)
In this paper, we determine the exact value of average n − K width
n(Wrpq(R), Lq(R)) of Sobolev-Wiener class Wrpq(R) in the metric Lq(R) for 1 > q ≥ p > ∞ and get the value of
n(Wrp(R), Lqp(R)) for the dual case. We also solve the optimal interpolation problems of Wrpq(R) in the metric Lq(R) and Wrp(R) in the metric Lqp(R) for 1 < q ≤ p < ∞. 相似文献
10.
Bimal Kumar Sinha 《Journal of multivariate analysis》1976,6(4):617-625
Treated in this paper is the problem of estimating with squared error loss the generalized variance | Σ | from a Wishart random matrix S: p × p Wp(n, Σ) and an independent normal random matrix X: p × k N(ξ, Σ Ik) with ξ(p × k) unknown. Denote the columns of X by X(1) ,…, X(k) and set ψ(0)(S, X) = {(n − p + 2)!/(n + 2)!} | S |, ψ(i)(X, X) = min[ψ(i−1)(S, X), {(n − p + i + 2)!/(n + i + 2)!} | S + X(1) X′(1) + + X(i) X′(i) |] and Ψ(i)(S, X) = min[ψ(0)(S, X), {(n − p + i + 2)!/(n + i + 2)!}| S + X(1) X′(1) + + X(i) X′(i) |], i = 1,…,k. Our result is that the minimax, best affine equivariant estimator ψ(0)(S, X) is dominated by each of Ψ(i)(S, X), i = 1,…,k and for every i, ψ(i)(S, X) is better than ψ(i−1)(S, X). In particular, ψ(k)(S, X) = min[{(n − p + 2)!/(n + 2)!} | S |, {(n − p + 2)!/(n + 2)!} | S + X(1)X′(1)|,…,| {(n − p + k + 2)!/(n + k + 2)!} | S + X(1)X′(1) + + X(k)X′(k)|] dominates all other ψ's. It is obtained by considering a multivariate extension of Stein's result (Ann. Inst. Statist. Math. 16, 155–160 (1964)) on the estimation of the normal variance. 相似文献
11.
Marco Buratti 《Journal of Combinatorial Theory, Series A》2000,90(2):353
A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a n-set {(ai, bi, ci, di) | i=1, …, n} of quadruples partitioning Z4n+1−{0} with the property that ni=1 {±(ai−ci), ±(bi−di)}=ni=1 {±(ai−bi), ±(ci−di)}=ni=1 {±(ai−di), ±(bi−ci)}=Z4n+1−{0}. The existence problem for Z-cyclic TWh(p)'s with p a prime has been solved for p1 (mod 16). I. Anderson et al. (1995, Discrete Math.138, 31–41) treated the case of p≡5 (mod 8) while Y. S. Liaw (1996, J. Combin. Des.4, 219–233) and G. McNay (1996, Utilitas Math.49, 191–201) treated the case of p≡9 (mod 16). In this paper, besides giving easier proofs of these authors' results, we solve the problem also for primes p≡1 (mod 16). The final result is the existence of a Z-cyclic TWh(v) for any v whose prime factors are all≡1 (mod 4) and distinct from 5, 13, and 17. 相似文献
12.
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)1 be a measurable function defined on a domain ΩRn, n2, and such that exp(βK(x))Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|nK(x)J(x,f) for a.e. xΩ and such that the Jacobian determinant J(x,f) is locally in L1 log−c1(n)βL. Then automatically J(x,f) is locally in L1 logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion. Namely, we obtain novel results on the size of removable singularities for bounded mappings of finite distortion, and on the area distortion under this class of mappings. 相似文献
13.
Bergeron N. 《Advances in Mathematics》1995,110(2)
We construct Families {ρl, kn} of orthogonal idempotents of the hyperoctahedral group algebras
[Bn], which commute with the Hochschild boundary operators bn=∑ni=0 (−1)idi. We show that those idempotents are projections onto some hyperoactahedral symmetric powers of the free Lie algebra Lie(l, k)n(
). The commutations above then decompose the Hochshild homology Hn(C) obtained by any functor C:Δop → K-module that factor through Fin′B, the hyperoctahedral category. Moreover, we show that this decomposition is the finest possible for any such functor. In particular, the Hochschild homology of a commutative algebra equipped with an involutive automorphism splits into components indexed by (l, k) and the corresponding Harrison homology splits into two components indexed by (0, 1) and (1, 0). Generalizing the Harrison complex, we show that H(l,k)n(C)Hn(Sh(l,k)./Sh(l−1, k+1)., where Sh(r,s).are some shuffle complexes associated to C. We also give the characters of the representations related to Lie(l, k)n(
) as a direct sum of induced characters. 相似文献
14.
T. Royen 《Journal of multivariate analysis》1991,38(2)
Three classes of expansions for the distribution function of the χk2(d, R)-distribution are given, where k denotes the dimension, d the degree of freedom, and R the “accompanying correlation matrix.” The first class generalizes the orthogonal series with generalized Laguerre polynomials, originally given by Krishnamoorthy and Parthasarathy [12]. The second class contains always absolutely convergent representations of the distribution function by univariate chi-square distributions and the third class provides also the probabilities for any unbounded rectangular regions. In particular, simple formulas are given for the three-variate case including singular correlation matrices R, which simplify the computation of third order Bonferroni inequalities, e.g., for the tail probabilities of max{χi2|1 ≤ i ≤ k} (k > 3). 相似文献
15.
Krzysztof Przes
awski 《Journal of Approximation Theory》1996,85(3):288-296
It is shown that for each convex bodyARnthere exists a naturally defined family
AC(Sn−1) such that for everyg
A, and every convex functionf: R→Rthe mappingy∫Sn−1 f(g(x)−y, x) dσ(x) has a minimizer which belongs toA. As an application, approximation of convex bodies by balls with respect toLpmetrics is discussed. 相似文献
16.
17.
Shichi Yamamoto 《Indagationes Mathematicae》1999,10(4):615
In this paper, we study numerical properties of Chern classes of certain covering manifolds. One of the main results is the following: Let ψ : X → Pn be a finite covering of the n-dimensional complex projective space branched along a hypersurface with only simple normal crossings and suppose X is nonsingular. Let ci(X) be the i-th Chern class of X. Then (i) if the canonical divisor KX is numerically effective, then (−1)kck(X) (k ≥ 2) is numerically positive, and (ii) if X is of general type, then (−1)ncil (X) cir, (X) > 0, where il + … + ir = n. Furthermore we show that the same properties hold for certain Kummer coverings. 相似文献
18.
We classify both the finite and infinite characters of the inductive limit symplectic group G. An important feature of our technique is the systematic use of a multiplicative structure on an “ordered completion” of the K0-group for the group C*-algebra A of G. We also give explicit examples of the K-theory for certain primitive quotients of A. 相似文献
19.
I. J. Schoenberg 《Journal of Approximation Theory》1983,39(4):324-337
Starting from the exponential Euler polynomials discussed by Euler in “Institutions Calculi Differentialis,” Vol. II, 1755, the author introduced in “Linear operators and approximation,” Vol. 20, 1972, the so-called exponential Euler splines. Here we describe a new approach to these splines. Let t be a constant such that t=|t|eiα, −π<α<π,t≠0,t≠1.. Let S1(x:t) be the cardinal linear spline such that S1(v:t) = tv for all v ε Z. Starting from S1(x:t) it is shown that we obtain all higher degree exponential Euler splines recursively by the averaging operation . Here Sn(x:t) is a cardinal spline of degree n if n is odd, while
is a cardinal spline if n is even. It is shown that they have the properties Sn(v:t) = tv for v ε Z. 相似文献
20.
If E is an ordered set, we study the processes Yt, t E, for which the vectorial spaces
t generated by all the conditional expectations E(Ysβ
t) for s ≥ t have finite dimensions d(t) ≤ N. (
t is some convenient filtration.) We first develop a geometrical approach in the general situation and give a “Goursat's representation” Yt = Σfi(t)Mi(t), where the Mi(t) are martingales. We then restrict us to the cases E =
or E =
2 and give representations of the processes by the mean of stochastic integrals of “Goursat's kernels.” The special case when Yt is the solution of a differential equation is considered. 相似文献