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1.
Let X=(X
t
,t) be a stationary Gaussian process on (, ,P), letH(X) be the Hilbert space of variables inL
2 (,P) which are measurable with respect toX, and let (U
s
,s) be the associated family of time-shift operators. We sayYH(X) (withE(Y)=0) satisfies the functional central limit theorem or FCLT [respectively, the central limit theorem of CLT if in [respectively,], where
相似文献
2.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
3.
On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
For 2-periodic functions
and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality
which takes into account the number of changes in the sign of the derivatives (x
(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p),
r
is the Euler perfect spline of degree r,
and
. The inequality indicated turns into the equality for functions of the form x(t) = a
r
(nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines. 相似文献
4.
On a finite segment [0, l], we consider the differential equation
5.
M. Katchalski 《Aequationes Mathematicae》1978,17(1):249-254
Denoting by dimA the dimension of the affine hull of the setA, we prove that if {K
i:i T} and {K
i
j
:i T} are two finite families of convex sets inR
n
and if dim {K
i
:i S} = dim {K
i
j
:i S}for eachS T such that|S| n + 1 then dim {K
i
:i T} = dim {K
i
: {i T}}. 相似文献
6.
G. A. Kalyabin 《Functional Analysis and Its Applications》2004,38(3):184-191
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
7.
Mark A. Pinsky 《Journal of Theoretical Probability》1993,6(1):187-193
A density functionf(x),xR
n
is said to bepiecewise smooth if for eachxR
n
, the mean value function
is piecewiseC
with compact support. (d is normalized surface measure on the unit sphere). The Fourier transform is
with spherical partial sum
.
Theorem. For suchf, lim
r
f
R
(x)=M
0+f(x) if and only ifrM
r
f(x) hask=[(n–3)/2] continuous derivatives. ([]=integer part). Otherwise we have lim
where 0 is uniquely determined. 相似文献
8.
Let (E
i
)
iI
be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E
i
)
iI
of spaces is
9.
Lower Bounds for Finite Wavelet and Gabor Systems 总被引:1,自引:0,他引:1
Given L
2(R) and a finite sequence {(a
r
,
r
)}
rR+XR consisting of distinct points, the corresponding wavelet system is the set of functions
. We prove that for a dense set of functions L
2(R) the wavelet system corresponding to any choice of {(a
r
,
r
)}
r
is linearly independent, and we derive explicite estimates for the corresponding lower (frame) bounds. In particular, this puts restrictions on the choice of a scaling function in the theory for multiresolution analysis. We also obtain estimates for the lower bound for Gabor systems
for functions g in a dense subset of L
2(R). 相似文献
10.
Summary We consider a (possibly) vector-valued function u: RN, Rn, minimizing the integral
, 2-2/(n*1)<p<2, whereD
i
u=u/x
i
or some more general functional retaining the same behaviour, we prove higher integrability for Du: D1 u,..., Dn–1 u Lp/(p-1) and Dnu L2; this result allows us to get existence of second weak derivatives: D(D1 u),...,D(Dn–1u)L2 and D(Dn u) L
p.This work has been supported by MURST and GNAFA-CNR. 相似文献
11.
B. J. C. Baxter 《Constructive Approximation》1991,7(1):427-440
In [4], deep results were obtained concerning the invertibility of matrices arising from radial basis function interpolation. In particular, the Euclidean distance matrix was shown to be invertible for distinct data. In this paper, we investigate the invertibility of distance matrices generated byp-norms. In particular, we show that, for anyp(1, 2), and for distinct pointsx
1,,x
n
d
, wheren andd may be any positive integers, with the proviso thatn2, the matrixA
n×n
defined by
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