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1.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
2.
Let
be an i.i.d. sequence of rotationally invariant random vectors in
. If X
12 is dominated (in the sense defined below) by Z2 for a rotationally invariant normal random vector Z in
, then for each k and
for p3 or p,n2 (resp. for 1p2, n3). The constant (
Zp)1/p is the best possible. The result applies, in particular, for variables uniformly distributed on the sphere S
n-1 or the ball B
n. In the case of the sphere, the best constant is
With this constant, the Khintchine type inequality in this case also holds for 1p2,n=2. 相似文献
3.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
4.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
5.
Let T be a regular operator from L
p L
p. Then
, where Tr denotes the regular norm of T, i.e., Tr=|T| where |T| denotes the modulus operator of a regular operator T. For p=1 every bounded linear operator is regular and T=Tr, so that the above inequality generalizes the Daugavet equation for operators on L
1–spaces. The main result of this paper (Theorem 9) is a converse of the above result. Let T be a regular linear operator on L
p and denote by T
A the operator TA. Then
for all A with (A)>0 if and only if
. 相似文献
6.
Paolo Cubiotti 《Set-Valued Analysis》1993,1(1):81-87
In this paper, we deal with the following generalized quasi-variational inequality problem: given a closed convex subsetX
n
, a multifunction :X 2
n
and a multifunction :X 2
X
, find a point (
) X ×
n
such that
We prove an existence theorem in which, in particular, the multifunction is not supposed to be upper semicontinuous. 相似文献
7.
Elena Prestini 《Monatshefte für Mathematik》1988,105(3):207-216
LetfL
p(
n
),n2, be a radial function and letS
Rf be the spherical partial sums operator. We prove that if
thenS
Rf(x)f(x) a.e. asR. The result is false for
and
\frac{{2n}}{{n + 1}}$$
" align="middle" border="0">
.Partially supported by M.P.I. 相似文献
8.
Let (X
t
) be a one dimensional diffusion corresponding to the operator
, starting from x>0 and T
0 be the hitting time of 0. Consider the family of positive solutions of the equation
with (0, ), where
. We show that the distribution of the h-process induced by any such is
, for a suitable sequence of stopping times (S
M
: M0) related to which converges to with M. We also give analytical conditions for
, where
is the smallest point of increase of the spectral measure associated to
. 相似文献
9.
The notion of the split extension of a commutative kinematic space is extended to the case of a weak K-loop with an incidence fibration (F, +,
). Theorem 1 states conditions under wich the quasi-direct productG F+
Q
with Aut(F, +) can be turned in a fibered incidence group (G,
, o) such that (F, +,
) becomes embeddable inG, and Theorem 2 the additional assumption such that (G,
, o) is even a kinematic space. In section 4, Theorem 3 shows that there are suitable examples of proper K-loops with an incidence fibration (derived from hyperbolic planes) on which one can apply Theorem 2.Dedicated to Erich Ellers on the occasion of his 70th birthdayResearch supported by M.U.R.S.T. 40% and by C.N.R. (G.N.S.A.G.A.) 相似文献
10.
Jelena V. Manojlović 《Czechoslovak Mathematical Journal》2005,55(1):41-60
New oscillation criteria are given for the second order sublinear differential equation
where a C
1 ([t
0, )) is a nonnegative function, , f C() with (x) 0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with [f(x) / #x03C8;(x)] 0 for x 0 and q C([t
0, )) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x (t) + q(t)x(t) = 0. 相似文献
11.
We study the reproducing kernel Hilbert spaces
with kernels of the form
where S(z1,z2) is a Schur function of two variables z
1,z2
. They are analogs of the spaces
with reproducing kernel (1-S(z)S(w)*)/(1-zw*) introduced by de Branges and Rovnyak l. de Branges and J. Rovnyak, Square Summable Power Series Holt, Rinehart and Winston, New York, 1966. We discuss the characterization of
as a subspace of the Hardy space on the bidisk. The spaces
form a proper subset of the class of the so–called sub–Hardy Hilbert spaces of the bidisk. 相似文献
)S(w_1 ,w_2 )^* }}{{(1 - z_1 w_1^* )(1 - z_2 w_2^* )}}$$ " align="middle" vspace="20%" border="0"> |
12.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1987,38(4):2081-2090
Let A={a1,...,an} and B={b1,...,bm} be systems of distinct points in
, let be a family of homotopic classes Hi,i=1,..., j+m, of closed Jordan curves on, where the classes Hj+l, l=1,...,m, consist of curves that are homotopic to a point curve in b. Let =1,..., j+m be a system of positive numbers and letU be the modulus of the extremal-metric problem for the family and the system . In this paper we investigate the dependence of the modulusU=U(,A,B) on the parameters i and on the disposition of the points ak and b. One shows thatU is a smooth function of the indicated arguments and one obtains expressions for the derivatives
U,
U, and
U. One gives some applications of these results.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 72–82, 1985. 相似文献
13.
Let
, the parameter space, be an open subset ofR
k
,k1. For each
, let the r.v.'sX
n
,n=1, 2,... be defined on the probability space (X, P
) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the -field of Borel subsets ofS. ForhR
k
and a sequence of p.d. normalizing matrices
n
=
n
k × k
(0 set
n
*
= * = 0 +
n
h, where 0 is the true value of , such that *,
. Let
n
(*, *)( be the log-likelihood ratio of the probability measure
with respect to the probability measure
, whereP
n
is the restriction ofP
over
n
= (X
1,X
2,...,X
n
. In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account. 相似文献
14.
Yimin Xiao 《Journal of Theoretical Probability》1997,10(4):849-866
Let X(t) (tR) be a real-valued centered Gaussian process with stationary increments. We assume that there exist positive constants
0, C
1, and c
2 such that for any tR and hR with |h|0
and for any 0r<min{|t|, 0}
where
is regularly varying at zero of order (0 < < 1). Let be an inverse function of near zero such that (s)=(s) log log(1/s) is increasing near zero. We obtain exact estimates for the weak -variation of X(t) on [0,a]. 相似文献
15.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
16.
The Jacobian conjecture for polynomial maps :K
n
K
n
is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra
of formal vector fields inn variables. To be precise, let
be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of
,H
the root spaces corresponding to linear forms onH and
. Then every polynomial map :K
n
K
n
with invertible Jacobian matrix is an automorphism if and only if every automorphism of
with (A)
satisfies (A)=A. 相似文献
17.
The main result is the following theorem. Let
be a commutative Banach algebra with radical R, where the factor algebra
is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rn1 /n 0 as n uniformly for r R, rl, then the algebra
is strongly decomposable, i.e., there exists a closed subalgebra B
isomorphic to
such that
=BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed
. There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967. 相似文献
18.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
19.
Suppose G is a connected, simple, real Lie group with
-rank(G) 2, M is an ergodic G-space with invariant probability measure , and : G × M Homeo(
) is a Borel cocycle. We use an argument of É. Ghys to show that there is a G-invariant probability measure on the skew product M ×
, such that the projection of to M is . Furthermore, if (G × M) Diff1(
), then can be taken to be equivalent to × , where is Lebesgue measure on
; therefore, is cohomologous to a cocycle with values in the isometry group of
. 相似文献
20.
We prove that the Sobolev embedding operator S
d,k,p :
, where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s
2 . 相似文献