共查询到20条相似文献,搜索用时 31 毫秒
1.
Rémi Vaillancourt 《Israel Journal of Mathematics》1972,13(1-2):225-231
This lecture gives an inside look into the proof of the continuity of pseudo-differential operators of orderm and typep, δ1, δ2 for 0≦p≦δ1=1, 0≦p≦δ2<1, andm/n≦p≦(δ1+δ2)/2. Applications are mentioned. 相似文献
2.
M. Abad J. P. Díaz Varela B. F. López Martinolich M. del C. Vannicola M. Zander 《Central European Journal of Mathematics》2006,4(4):547-561
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L
p,k, and the finite field F(p
k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L
p,k) generated by L
p,k into the variety V(F(p
k)) generated by F(p
k) and an interpretation Φ2 of V(F(p
k)) into V(L
p,k) such that Φ2Φ1(B) = B for every B ε V(L
p,k) and Φ1Φ2(R) = R for every R ε V(F(p
k)). 相似文献
3.
LetM=(W, d) be a metric space. LetL
1 denote theL
1 metric. AnL
1-embedding ofM into Cartesiank-space ℝ
k
is a distance-preserving map from (W, d) into (ℝ
k
,L
1). Letc(k) be the smallest integer such that for every metric spaceM, M isL
1-embeddable inR
k iff everyc(k)-sized subspace ofM isL
1-embeddable inR
k. A special case of a theorem of Menger (see p. 94 of [5]) says thatc(1) exists and equals 4. We show thatc(2) exists and satisfies 6≦c(2)≦11. Whether or notc(k) exists for anyk≧3 is an open question.
The research of S. M. Malitz was partially supported by NSF Grant CCR-8909953. 相似文献
4.
Aregression is a functiong from a partially ordered set to itself such thatg(x)≦x for allz. Amonotone k-chain is a chain ofk elementsx
1<x
2 <...<x
k
such thatg(x
1)≦g(x
2)≦...≦g(x
k
). If a partial order has sufficiently many elements compared to the size of its largest antichain, every regression on it
will have a monotone (k + 1)-chain. Fixingw, letf(w, k) be the smallest number such that every regression on every partial order with size leastf(w, k) but no antichain larger thanw has a monotone (k + 1)-chain. We show thatf(w, k)=(w+1)
k
.
Dedicated to Paul Erdős on his seventieth birthday
Research supported in part by the National Science Foundation under ISP-80-11451. 相似文献
5.
M. Capon 《Israel Journal of Mathematics》1980,36(3-4):346-364
In this article we show that if 1<p, r<∞, the spaceL
p
(l
r
) is primary. If we let (h
k
) be the Haar system inL
p
and (e
i
) the usual base ofl
r
, we give sufficient conditions on a subsequence of (h
k
⊗e
i
)
k ≧1,i≧1 for it to generate a space isomorphic toL
p
(l
r
). We deduce the primarity ofL
p
(l
r
).
相似文献
6.
Tamar Burak 《Israel Journal of Mathematics》1972,12(1):79-93
Let A be the closed unbounded operator inL
p(G) that is associated with an elliptic boundary value problem for a bounded domainG. We prove the existence of a spectral projectionE determined by the set Γ = {λ;θ
1≦argλ≦θ
2} and show thatAE is the infinitesimal generator of an analytic semigroup provided that the following conditions hold: 1<p<∞; the boundary
ϖΓ of Γ is contained in the resolvent setp(A) ofA;π/2≦θ<θ
2≦3π/2 ; and there exists a constantc such that (I)││(λ-A)-1││≦c/│λ│ for λ∈ϖΓ. The following consequence is obtained: Suppose that there exist constantsM andc such that λ∈p(A) and estimate (I) holds provided that |λ|≧M and Re λ=0. Then there exist bounded projectionE
− andE
+ such thatA is completely reduced by the direct sum decompositionL
p(G)=E−Lp (G) ⊕E+Lp (G) and each of the operatorsAE
− and—AE
+ is the infinitestimal generator of an analytic semigroup. 相似文献
7.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
8.
A. Arias 《Israel Journal of Mathematics》1988,63(2):139-148
We show that for 1 ≦p < ∞,p ≠ 2, ifɛ > 0 is small enough andX ≦L
p is the span ofn independent Rademacher functions orn independent Gaussian random variables, then any superspaceY ofX satisfyingd(Y,L
p
m
) ≦ 1 +ɛ has dimension larger thanr
n, wherer =r(ɛ, p) > 1.
This forms part of the author’s doctoral dissertation prepared at Texas A&M University under the direction of Professor W.
B. Johnson.
Supported in part by NSF DMS-85 00764. 相似文献
9.
《Arkiv f?r Matematik》1992,30(1):217-220
We determine the smallest Schatten class containing all integral operators with kernels inL
p(Lp', q)symm, where 2 <p∞ and 1≦q≦∞. In particular, we give a negative answer to a problem posed by Arazy, Fisher, Janson and Peetre in [1].
Supported in part by DGICYT (SAB-90-0033). 相似文献
10.
David Gilat 《Israel Journal of Mathematics》1988,63(3):270-280
For eachp>1, the supremum,S, of the absolute value of a martingale terminating at a random variableX inL
p, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1).The maximum,M, of a mean-zero martingale which starts at zero and terminates atX, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1), whereσ
q is the unique solution of the equationt = ‖Z −t ‖
q
for an exponentially distributed random variableZ with mean 1.σ
p has other characterizations and satisfies lim
p‖
q
− 1
σ
q =c withc determined byce
c+1 = 1. Equalities in (1) and (2) are attainable by appropriate martingales which can be realized as stopped segments of Brownian
motion. A presumably new property of the exponential distribution is obtained en route to inequality (2). 相似文献
11.
Let Γ be a regular curve and Lp(Γ),1<p<+∞, be the class of all complex-valued functions f defined on Γ which are such that |f|p is integrable in sense of Lebesgue. In this work, we define the kth p-Faber polynomial Fk.p(z), the kth p-Faber principle part ≈Fk.p(1/z) for Γ, and defined the nth p-Faber-Laurent rational function Rn,p(f, z) and p-generalized modulus of continuity Ωp of a function f of Lp(Γ). We investigate some properties of Fk.p(z) and ≈Fk.p(1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ωp in the mean of functions of Lp(Γ) by the rational functions Rn.p(.,z). 相似文献
12.
We investigate the asymmetry, gl constants and best factorization estimates of then-dimensional spaces of polynomialsH
p
n
=span{e
ikx;k=1,2,…,n} equipped with theL
p norm for 1≦p≦∞.
Supported in part by NSF grant # MCS-8109561. 相似文献
13.
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
14.
It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p
n}, 1≦p
n<∞,p
n→p, the spaceX=(Σ⊕l
p
n)
q
(resp.U=(Σ⊕L
p
n(0, 1))
q
) is uniformly homeomorphic toX⊕l
p (resp.U⊕L
p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent. 相似文献
15.
Best trigonometric approximation in L
p
, 1≦p≦∞, is characterized by a modulus of smoothness, which is equivalent to zero if the function is a trigonometric polynomial
of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses
properties similar to those of the classical one. 相似文献
16.
Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate analytic
semigroups of linear operators onL
p(R
n
), 1≦p≦∞. An explicit characterization of the domain is given for 1<p<∞. An application to parabolic problems is also included.
This work has been partially supported by the Research Funds of the Ministero della Pubblica Istruzione.
The authors are members of GNAFA (Consiglio Nazionale delle Ricerche). 相似文献
17.
The Fast Johnson–Lindenstrauss Transform (FJLT) was recently discovered by Ailon and Chazelle as a novel technique for performing
fast dimension reduction with small distortion from ℓ
2
d
to ℓ
2
k
in time O(max {dlog d,k
3}). For k in [Ω(log d),O(d
1/2)], this beats time O(dk) achieved by naive multiplication by random dense matrices, an approach followed by several authors as a variant of the seminal
result by Johnson and Lindenstrauss (JL) from the mid 1980s. In this work we show how to significantly improve the running
time to O(dlog k) for k=O(d
1/2−δ
), for any arbitrary small fixed δ. This beats the better of FJLT and JL. Our analysis uses a powerful measure concentration bound due to Talagrand applied
to Rademacher series in Banach spaces (sums of vectors in Banach spaces with random signs). The set of vectors used is a real
embedding of dual BCH code vectors over GF(2). We also discuss the number of random bits used and reduction to ℓ
1 space.
The connection between geometry and discrete coding theory discussed here is interesting in its own right and may be useful
in other algorithmic applications as well. 相似文献
18.
Michele Capon 《Israel Journal of Mathematics》1982,42(1-2):87-98
In this article we show thatL
p(L
r) is primary forp andr in ]1,+∞[. If (h
k)
k≧1 denote the Haar basis, we begin with a study of the sequence (h
k ⊗h
i) and, in particular, the space generated by a subsequence of this sequence. In the first part we study the base ofL
p(L
r) and in the second part we show that this space is primary. 相似文献
19.
LetF be a collection ofk-element sets with the property that the intersection of no two should be included in a third. We show that such a collection
of maximum size satisfies .2715k+o(k)≦≦log2 |F|≦.7549k+o(k) settling a question raised by Erdős. The lower bound is probabilistic, the upper bound is deduced via an entropy argument.
Some open questions are posed.
This research has been supported in part by the Office of Naval Research under Contract N00014-76-C-0366.
Supported in part by a NSF postdoctoral Fellowship. 相似文献
20.
Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω1(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω1(P) ≦ Z(P) and N
G
(Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result.
This paper was partly supported by Hungarian National Foundation for Scientific Research Grant # T049841 and T038059. 相似文献