共查询到20条相似文献,搜索用时 31 毫秒
1.
Karl Umgeher 《Monatshefte für Mathematik》1976,100(1):311-314
We consider the set of regular functions
H = { f:f = z + ?n = 2¥ nbn zn ,|bn | \leqslant 1} on |z| < 1H = \{ f:f = z + \sum\limits_{n = 2}^\infty {nb_n z^n ,|b_n |{\mathbf{ }} \leqslant 1\} {\mathbf{ }}} on{\mathbf{ }}|z|{\mathbf{ }}< {\mathbf{ }}1
. We construct a Borel measure and a class of outer measures
h
onH. With these and
h
we show that: (HS)=0 and
h
(HS)=0, (S is the set of normed univalent functions). From
h
(HS)=0 follows—forh=t
—that the Hausdorff—Billingsley-dimension ofHS is zero. 相似文献
2.
3.
Gyula Pap 《Journal of Theoretical Probability》1990,3(4):563-577
If
a,T
is a Gaussian measure on a Hilbert space with meana and covariance operatorT, andr is a fixed positive number, then the functiong(a,T)=
a,T
{xr} satisfies the equation
相似文献
4.
5.
Torleiv Kløve 《BIT Numerical Mathematics》1972,12(3):342-346
Let(n) be the least integer such thatn may be represented in the formn=x
1
2
+x
2
3
+...+x
(n)
(n)+1 wherex
1,x
2, ...,x
(n) are natural numbers. We computed(n) forn 250 000 and found that(n) 5 for all thesen exceptn=56, 160 for which(n)=6. Also(n) 4 for 41542<n<=250 000. 相似文献
6.
Joachim Mahnkopf 《Compositio Mathematica》2000,124(3):253-304
Let be a cuspidal automorphic representation of GL3(
), unramified at pand of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions on
p
*
having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |(U)|
p
|Haar(U)|
p
for open subsets U
p
*, where Haardenotes the invariant distribution on
p
*. 相似文献
7.
A radial basis function approximation has the form where:R
d
R is some given (usually radially symmetric) function, (y
j
)
1
n
are real coefficients, and the centers (x
j
)
1
n
are points inR
d
. For a wide class of functions , it is known that the interpolation matrixA=((x
j
–x
k
))
j,k=1
n
is invertible. Further, several recent papers have provided upper bounds on ||A
–1||2, where the points (x
j
)
1
n
satisfy the condition ||x
j
–x
k
||2,jk, for some positive constant . In this paper we calculate similar upper bounds on ||A
–1||2 forp1 which apply when decays sufficiently quickly andA is symmetric and positive definite. We include an application of this analysis to a preconditioning of the interpolation matrixA
n
= ((j–k))
j,k=1
n
when (x)=(x
2+c
2)1/2, the Hardy multiquadric. In particular, we show that sup
n
||A
n
–1
|| is finite. Furthermore, we find that the bi-infinite symmetric Toeplitz matrix enjoys the remarkable property that ||E
–1||
p
= ||E
–1||2 for everyp1 when is a Gaussian. Indeed, we also show that this property persists for any function which is a tensor product of even, absolutely integrable Pólya frequency functions.Communicated by Charles Micchelli. 相似文献
8.
Flemming Topsøe 《manuscripta mathematica》1976,19(1):1-14
Two problems will be considered. In Part I we consider a class of subsets of a topological space X and a Radon measure on X; if it is known that, for sufficiently many
, the restrictions of the sets in constitutes a uniformity class in T w.r.t. the restriction of the given measure, then we ask if it follows that is a uniformity class in X.Part II, which can be read independently of Part I, is concerned with the question whether, to a given convergent sequence of Radon measures, say n, there always exist sufficiently many compact sets K such that n(K)(K). 相似文献
9.
It is shown that some well-known properties of the Sobolev spaceL
p
l
() do not admit extension to the spaceL
p
l
() of the functions withl-th order derivatives inL
p
(),l>1, without requirements to the domain . Namely, we give examples of such that
10.
Perturbation of Dirichlet forms by measures 总被引:8,自引:0,他引:8
Perturbations of a Dirichlet form
by measures are studied. The perturbed form
––++ is defined for – in a suitable Kato class and + absolutely continuous with respect to capacity. L
p-properties of the corresponding semigroups are derived by approximating – by functions. For treating +, a criterion for domination of positive semigroups is proved. If the unperturbed semigroup has L
p
-L
q
-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic on L
1 the same is shown to be true for the perturbed semigroup, for a large class of measures. 相似文献
11.
M.-R. Skrzipek 《BIT Numerical Mathematics》2004,44(2):291-306
Let {x
}=0,...,n
be a set of distinct nodes, and let {p
n
}
n0 be a sequence of polynomials, degp
n
=n, whose elements satisfy a three-term recurrence relation. We derive explicit representations for the inverse of a Vandermonde-like matrix V
n
=(p
(x
)),=0,...,n
and present some numerical results. 相似文献
12.
Riddhi Shah 《Journal of Theoretical Probability》1991,4(2):391-405
We show that any infinitely divisible measure on ap-adic algebraic group (p a prime) has a translatex, by an elementx centralizing the support of , such thatx can be embedded in a continuous real one-parameter semigroup {V
t
}
t
>0, asx=v
1. 相似文献
13.
14.
A -hyperfactorization ofK
2n
is a collection of 1-factors ofK
2n
for which each pair of disjoint edges appears in precisely of the 1-factors. We call a -hyperfactorizationtrivial if it contains each 1-factor ofK
2n
with the same multiplicity (then =(2n–5)!!). A -hyperfactorization is calledsimple if each 1-factor ofK
2n
appears at most once. Prior to this paper, the only known non-trivial -hyperfactorizations had one of the following parameters (or were multipliers of such an example)
15.
Greg Budzban 《Journal of Theoretical Probability》1994,7(3):635-646
Given a sequence of probability measures (
n
) on a finite abelian semigroup, we present necessary and sufficient conditions which guarantee the weak convergence of the convolution products
k,n
k+1*···*
n
(k<n), asn for allk0. These conditions are verifiable in the sense that they are based entirely on the individual measures in the sequence (
n
). 相似文献
16.
Let áA, B | Am=1, Bn=At, BAB-1=Ar?\langle A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB^{-1}=A^\rho\rangle
where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d. 相似文献
17.
LetK
p(u1, ..., up) be the completep-partite graph whoseith vertex class hasu
i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1>1/r, every graphG=G
n of sufficiently large order |G|=n with at least
|