共查询到20条相似文献,搜索用时 31 毫秒
1.
E. Csáki 《Probability Theory and Related Fields》1980,54(3):287-301
Summary Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup ¦W(xT)(2T loglog T)–1/2–f(x)¦, 0x1 suitably normalized as T.This extends Chung's result valid for f(x)0, stating that lim inf.[ sup ¦(2T loglogT)–1/2
W(xT)¦(loglog T)–1]=/4 a.s. T 0x1 相似文献
2.
LetH=(A, B) be a pair of HermitianN×N matrices. A complex number is an eigenvalue ofH ifdet(A–B)=0 (we include = ifdetB=0). For nonsingularH (i.e., for which some is not an eigenvalue), we show precisely which eigenvalues can be characterized as
k
+
=sup{inf{*A:*B=1,S},SS
k},S
k being the set of subspaces of C
N
of codimensionk–1.Dedicated to the memory of our friend and colleague Branko NajmanResearch supported by NSERC of Canada and the I.W.Killam FoundationProfessor Najman died suddenly while this work was at its final stage. His research was supported by the Ministry of Science of CroatiaResearch supported by NSERC of Canada 相似文献
3.
Marilyn Breen 《Monatshefte für Mathematik》1996,122(1):1-7
LetS be a finite union of boxes inR
d
. Forx inS, defineA
x
={yx is clearly visible fromy via staircase paths inS}, and let KerS denote the staircase kernel ofS. Then KerS={A
x
x is a point of local nonconvexity ofS}. A similar result holds with clearly visible replaced by visible and points of local nonconvexity ofS replaced by boundary points ofS.Supported in part by NSF grant DMS-9207019. 相似文献
4.
We prove that if the indicator-function1
E
of a measurable setE is a Fourier multiplier in the spaceE
p
() for somep2 thenE is an open set (up to a set of measure zero). 相似文献
5.
Let be an infinitely divisible probability measure onR
n
without Gaussian component and let be its Lévy measure. Suppose that is absolutely continuous with respect to the Lebesgue measure . We investigate the structure of the set
n
of admissible translates of . This yields a unified presentation of previously known results. We also show that if(S)>0 then is equivalent to , under the assumption that supp =R
n
, whereS is the closure of the semigroup generated by the support of .The research of this author is supported by KBN Grant.The research of this author is supported by AFSOR Grant No. 90-0168, and the University of Tennessee Science Alliance, a State of Tennessee Center of Excellence. 相似文献
6.
Bianca Di Blasio 《Monatshefte für Mathematik》1997,123(1):21-42
Letn=vz be anH-type group, and letna be the harmonic semidirect product ofn withaR. LetNA be the corresponding simply connected Lie group. If dimv=m and dimz=k, denoteQ=m/2+k. We prove that the spherical Fourier transform is a topological isomorphism between thep-Schwartz spacel
p
(N,A),(0<p2), (0<p2), and the space of holomorphic rapidly decreasing functions on the strip {sC:|Re(s)|<Q/2} with =2/p–1. 相似文献
7.
Let be a positive Radon measure in R
n with compact support
. Let Q
jm
be cubes with side-length
2-j+1 originating from the canonical tiling of R
n where j\in N
0
and m\in Z
n. If \in R, 0 < p \le
, 0 < q \le , then
pq
is the mixed
q
–
p
-quasi-norm of the sequence 2
j
(Q
jm
). Quantities of this type are considered in fractal geometry
(multifractal formalism) and in the theory of the
function spaces B
s
pq
(R
n) and F
s
pq
(R
n).
In Theorem 1 we deal with the question when
pq
is an equivalent quasi-norm in some of these spaces (-property). If
|| = 0, then
S
consists of those points
(t,s) in the t–s-diagram in Figure 1 for which belongs to
B
s
p (R
n) with pt = 1.
Theorem 2 deals
with the interrelation of S
and
pq
. Some
applications to truncated Riesz potentials, Bessel potentials
and Fourier transforms of are given. 相似文献
8.
M. Sh. Shabozov 《Ukrainian Mathematical Journal》1995,47(11):1769-1778
For the classB
p
, 0 < 1, 1p , of 2-periodic functions of the form f(t)=u(,t), whereu (,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel K(t) of the convolution f= K *g, gl, with respect to the metric of L1. We also consider the problem of renewal of the values of the convolution operator by using the information about the values of the boundary functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 11, pp. 1549–1557, November, 1995. 相似文献
9.
JirÍ Adámek 《Applied Categorical Structures》1996,4(1):121-126
For a topological category over Set we prove that if a functor T: has a fixed cardinal (i.e. for each object K with card (UK)= we have card (UTK)), then T has a least fixed point, and if T has a successive pair of fixed cardinals and +, then T has a greatest fixed point. This extends results of Adámek and Koubek.Partial financial support of the Grant Agency of the Czech Republic under Grant No. 201/93/0950 is gratefully acknowledged. 相似文献
10.
A. N. Bakhvalov 《Analysis Mathematica》2001,27(1):3-36
Let a ={nlna (n+1)}, where a R. The following results are established: For every &fnof a BV ((- ]2), the triangular partial sums of its Fourier series are uniformly bounded if a = -1, and converge everywhere if a < -1.For every a>0, there exists &fnof a BV ((- ]2) such that the triangular partial sums of its Fourier series are unbounded at the point (0;0). 相似文献
11.
Summary It is proved that the operatorP: L
1 (0, ) L
1(0, ), given byPg(z) =
z/c
[g(x)/cx]dx, is completely mixing, i.e.,P
n
g
1 0 forg L
1(0, ) with g dx = 0. This implies that, forc (0, 1), each continuous and bounded solution of the equationf(x)=
0
cx
f(t)dt/(cx) (x (0, 1]) is constant. 相似文献
12.
Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(1):49-55
For families of probability measures (P
, )) generated by semimartingales, we consider the local density)(y, )=
t
(y, ))
t0 of a, measureP
y
with respect to the measureP
whose logarithm is the difference of a local martingale and a positive predictable increasing locally bounded process. Conditions are obtained under which the relations
and
hold, wherey
t
depends in some way ont, while
t
ast . Applications of these relations are exhibited and an example is given when the hypotheses of the theorems proved can be verified.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 48–55, 1986. 相似文献
13.
The aim of the present paper is to solve some major open problems of Hilbert C*-module theory by applying various aspects of multiplier C*-theory. The key result is the equivalence established between positive invertible quasi-multipliers of the C*-algebra of compact operators on a Hilbert C*-module {, ., } and A-valued inner products on , inducing an equivalent norm to the given one. The problem of unitary isomorphism of C*-valued inner products on a Hilbert C*-module is considered and new criteria are formulated. Countably generated Hilbert C*-modules turn out to be unitarily isomorphic if they are isomorphic as Banach C*-modules. The property of bounded module operators on Hilbert C*-modules of being compact and/or adjointable is unambiguously connected to operators with respect to any choice of the C*-valued inner product on a fixed Hilbert C*-module if every bounded module operator possesses an adjoint operator on the module. Every bounded module operator on a given full Hilbert C*-module turns out to be adjointable if the Hilbert C*-module is orthogonally complementary. Moreover, if the unit ball of the Hilbert C*-module is complete with respect to a certain locally convex topology, then these two properties are shown to be equivalent to self-duality. 相似文献
14.
M. V. Litvinova 《Algebra and Logic》1994,33(3):142-146
The question as to whether a product of two finitely based varieties of lattice-ordered groups is finitely based is considered. It is proved that varieties
and
are finitely based; here
is a variety of lattice-ordered groups defined by identities [x
n,y
n] =e and [[x,y] z, [x
1,y
1] z
1] =e;
is a variety of lattice-ordered nilpotent groups of class s, defined by an identity [x
1,x
2,...,x
(s+1)] =e; V is an arbitrary finitely based variety of lattice-ordered groups.
Translated fromAlgebra i Logika, Vol. 33, No. 3, pp. 255–263, May–June, 1994.Supported by the Russian Foundation for Fundamental Research, grant No. 93-011-1524. 相似文献
15.
Hiroaki Taniguchi 《Geometriae Dedicata》2000,80(1-3):99-123
Let k, K be fields, and assume that |k| 4 and n, m 2, or |k| = 3 and n 3, m 2. Then, for any embedding of AG(n, k) into PG(m, K), there exists an isomorphism from k into K and an (n+1) × (m+1) matrix B with entries in K such that can be expressed as (x1,x2,...,xn) = [(1,x1
,x2
,...,xn
)B], where the right-hand side is the equivalence class of (1,x1
,x2
,...,xn
)B. Moreover, in this expression, is uniquely determined, and B is uniquely determined up to a multiplication of element of K*. Let l 1, and suppose that there exists an embedding of AG(m+l, k) into PG(m, K) which has the above expression. If we put r = dim
k
K, then we have r 3 and m > 2 l-1)/(r-2). Conversely, there exists an embedding of AG(l+m, k) into PG(m, K) with the above expression if K is a cyclic extension of k
with dim
k
K=r 3, and if m 2l/(r-2) with m even or if m 2l/(r-2) +1 with m odd. 相似文献
16.
Summary Using the Isaacs-Zimmermann's theory of iterative roots of functions, we prove a theorem concerning the problemP 250 posed by J. Tabor:Letf: E E be a given mapping. Denote byF the set of all iterative roots off. InF we define the following relation: if and only if is an iterative root of. The relation is obviously reflexive and transitive. The question is: Is it also antisymmetric? If we consider iterative roots of a monotonic function the answer is yes. But in general the question is open.Here we prove that there exists a three-element decomposition {
i
;i = 1, 2, 3} of the setE
E
with blocks i of the same cardinality 2cardE
such that the functions from 1 do not possess any proper iterative root, the quasi-ordering is not antisymmetric onF(f) for anyf 2, and is an ordering onF(f) for anyf 3. Iff is a strictly increasing continuous self-bijection ofE, then the relation is an ordering onF(f) ifff is different from the identity mapping of the setE. 相似文献
17.
An invariant based on orderedK-theory with coefficients in
n>1 /n and an infinite number of natural transformations has proved to be necessary and sufficient to classify a large class of nonsimple C* -algebras. In this paper, we expose and explain the relations between the order structure and the ideals of the C* -algebras in question.As an application, we give a new complete invariant for a large class of approximately subhomogeneous C*-algebras. The invariant is based on ordered K-theory with coefficients in /. This invariant is more compact (hence, easier to compute) than the invariant mentioned above, and its use requires computation of only four natural transformations. 相似文献
18.
Jacques Simon 《Annali di Matematica Pura ed Applicata》1986,146(1):65-96
Summary A characterization of compact sets in Lp (0, T; B) is given, where 1P and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space Lp (0,T; B) from estimates with values in some spaces X, Y or B where XBY with compact imbedding XB. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {fn} is bounded in Lq(0,T; B) and in L
loc
1
(0, T; X) and if {fn/t} is bounded in L
loc
1
(0, T; Y) then {fn} is relatively compact in Lp(0,T; B), p相似文献
19.
Given ringsR with prime power characteristicp
k
, quasivarieties (R) of lattices generated by lattices of submodules ofR-modules are studied. An algebra of expressionsd not dependent onR is developed, such that each suchd uniquely determines a two-sides ideald
R
ofR. The main technical result is that (R)
(S) makes all implications of the formd
s
=S dR=R true, for any such expressiond. The proof makes use of the known equivalence between (R)
(S) and existence of an exact embedding functorR-Mod S
-Mod. Fork 2, the ordered setW(p
k
) of all lattice quasivarieties (R),R having characteristic p
K
, is shown to be large and complicated, with ascending and descending chains and antichains having continuously many elements. More precisely,W(p
k
) has a subset which is order isomorphic to the Boolean algebra of all subsets of a denumerably infinite set. Also, given any prime powerp
k
,k 2, a ringR can be constructed so that (R) and (R
op) for the opposite ringR
op are distinct elements ofW(p
k
).Presented by R. Freese.Research partially supported by Hungarian National Foundation for Scientific Research grant no. 1903. 相似文献
20.
M. Akkouchi 《Periodica Mathematica Hungarica》1994,29(2):127-136
Let be a Guelfand measure (cf. [A, B]) on a locally compact groupG DenoteL
1
(G)=*L
1(G)* the commutative Banach algebra associated to . We show thatL
1
(G) is semi-simple and give a characterization of the closed ideals ofL
1
(G). Using the -spherical Fourier transform, we characterize all linear bounded operators inL
1
(G) which are invariants by -translations (i.e. such that
1((
x
f)
)=(
x
((f))
for eachxG andfL
1
(G); where
x
f(y)=f(xy); x,y G). WhenG is compact, we study the algebraL
1
(G) and obtain results analogous to ones obtained for the commutative case: we show thatL
1
(G) is regular, all closed sets of its Guelfand spectrum are sets of synthesis and establish theorems of harmonic synthesis for functions inL
p
(G) (p=1,2 or +). 相似文献