共查询到20条相似文献,搜索用时 31 毫秒
1.
B. Greuel 《Archiv der Mathematik》2000,75(2):121-124
Suppose that f1, ?, fmf_1, \ldots , f_m satisfy functional equations of type¶¶ fi(zd) = Pi(z, fi(z)) or fi(z) = Pi(z, fi(zd))f_i({z^d}) = P_i(z, f_i(z)) \quad {or} \quad f_i(z) = P_i(z, f_i({z^d})) ¶for i = 1, ?, mi = 1, \ldots , m, an integer d > 1 and polynomials Pi ? \Bbb C (z)[ y]P_i \in \Bbb C (z)[ {y}] with pairwise distinct partial degrees degy( P1), ?, degy( Pm)\deg _y( {P_1}), \ldots , \deg _y( {P_m}). Generalizing a result of Keiji Nishioka and using an idea of Kumiko Nishioka we show, that f1, ?, fmf_1, \ldots , f_m can only be algebraically dependent over \Bbb C (z)\Bbb C (z), if there is an index k ? { 1, ?, m}\kappa \in \{ {1, \ldots , m}\} such that fkf_{\kappa } is rational. 相似文献
2.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
3.
We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle
where f(Z)=(f(z1), …, f(l1)(z1), …, f(zm), …, f(lm)(zm)), A is a M×M positive definite matrix or a positive semidefinite diagonal block matrix, M=l1+…+lm+m, dμ belongs to a certain class of measures, and |zi|>1, i=1, 2, …, m. 相似文献
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4.
Nadia J. Gal James E. Jamison Aristomenis G. Siskakis 《Complex Analysis and Operator Theory》2010,4(2):245-255
We are interested in the isometric equivalence problem for the Cesàro operator
C(f) (z) = \frac1z ò0zf(x) \frac11-xd x{C(f) (z) =\frac{1}{z} \int_{0}^{z}f(\xi) \frac{1}{1-\xi}d \xi} and an operator
Tg(f)(z)=\frac1zò0zf(x) g¢(x) d x{T_{g}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\xi) g^{\prime}(\xi) d \xi}, where g is an analytic function on the disc, on the Hardy and Bergman spaces. Then we generalize this to the isometric equivalence
problem of two operators Tg1{T_{g_{1}}} and Tg2{T_{g_{2}}} on the Hardy space and Bergman space. We show that the operators Tg1{T_{g_{1}}} and Tg2{T_{g_{2}}} satisfy Tg1U1=U2Tg2{T_{g_{1}}U_{1}=U_{2}T_{g_{2}}} on H
p
, 1 ≤ p < ∞, p ≠ 2 if and only if g2(z) = lg1(eiqz){g_{2}(z) =\lambda g_{1}(e^{i\theta}z) }, where λ is a modulus one constant and U
i
, i = 1, 2 are surjective isometries of the Hardy Space. This is analogous to the Campbell-Wright result on isometrically equivalence
of composition operators on the Hardy space. 相似文献
5.
F. M. Al-Oboudi 《Complex Analysis and Operator Theory》2011,5(3):647-658
Let A denote the class of analytic functions f, in the open unit disk E = {z : |z| < 1}, normalized by f(0) = f′(0) − 1 = 0. In this paper, we introduce and study the class STn,al,m(h){ST^{n,\alpha}_{\lambda,m}(h)} of functions f ? A{f\in A}, with
\fracDn,al fm(z)z 1 0{\frac{D^{n,\alpha}_\lambda f_m(z)}{z}\neq 0}, satisfying
\fracz(Dn,al f(z))¢Dn,al fm(z)\prec h(z), z ? E,\frac{z\left(D^{n,\alpha}_\lambda f(z)\right)'}{D^{n,\alpha}_\lambda f_m(z)}\prec h(z),\quad z\in E, 相似文献
6.
We study a problem related to coin flipping, coding theory, and noise sensitivity. Consider a source of truly random bits x ∈ {0, 1}n, and k parties, who have noisy version of the source bits yi ∈ {0, 1}n, when for all i and j, it holds that P [y = xj] = 1 ? ?, independently for all i and j. That is, each party sees each bit correctly with probability 1 ? ?, and incorrectly (flipped) with probability ?, independently for all bits and all parties. The parties, who cannot communicate, wish to agree beforehand on balanced functions fi: {0, 1}n → {0, 1} such that P [f1(y1) = … = fk(yk)] is maximized. In other words, each party wants to toss a fair coin so that the probability that all parties have the same coin is maximized. The function fi may be thought of as an error correcting procedure for the source x. When k = 2,3, no error correction is possible, as the optimal protocol is given by fi(yi) = y. On the other hand, for large values of k, better protocols exist. We study general properties of the optimal protocols and the asymptotic behavior of the problem with respect to k, n, and ?. Our analysis uses tools from probability, discrete Fourier analysis, convexity, and discrete symmetrization. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
7.
Chuan Jen Chyan 《Journal of Difference Equations and Applications》2013,19(5):403-413
Values of λ are determined for which there exist positive solutions of the 2mth order differential equation on a measure chain, (-1)m x ?2m (t)=λa(t)f(u(σ(t))), y? [0,1], satisfying α i+1 u ?21(0)+0, γ i+1 u ?21(σ(1))=0, 0≤i≤m?1 with αi,βi,γi,δi≥0, where a and f are positive valued, and both lim x-0+ (f(x)/x) and lim x-0+ (f(x)/x) exist. 相似文献
8.
Edmund Hlawka 《Geometriae Dedicata》1992,44(1):105-110
We denote with PC
m the m-dimensional complex projective space, with U the unitary group acting on it with z
i(j=0, 1,..., m) the homogenous coordinates of a point [z] of PC
m and assume that the z
i are normalized such that z
0z0 +...+z
mzm=1. Furthermore we denote the U-invariant metric on PC
m with d. We consider now a uniformly distributed sequence ([z]
k
; k=1,2,...) of points on PC
m and study the sequence (d
l([z]
k
, [z]0)), l0, [z]0 a fixed point. We prove with the help of the theory of uniform distribution properties of this sequence. We consider furthermore a dual sequence suggested by the theory of H. Weyl and L. V. Ahlfors on meromorphic curves. 相似文献
9.
Jerzy Szulga 《Probability Theory and Related Fields》1992,94(1):83-90
Summary If (Y
i) and (V
i) are independent random sequences such thatY
i are i.i.d. random variables belonging to the normal domain of attraction of a symmetric -stable law, 0<<2, andV
i are i.i.d. random variables, then the limit distributions of U-statistics
, coincide with the probability laws of multiple stochastic integralsX
d
f = ...
f (t
1, ... ,t
d)dX(t
d) with respect to a symmetric -stable processX(t).The research was originated during author's visit at ORIE, Cornell University 相似文献
10.
Massimo Fornasier Karin Schnass Jan Vybiral 《Foundations of Computational Mathematics》2012,12(2):229-262
Let us assume that f is a continuous function defined on the unit ball of ℝ
d
, of the form f(x)=g(Ax), where A is a k×d matrix and g is a function of k variables for k≪d. We are given a budget m∈ℕ of possible point evaluations f(x
i
), i=1,…,m, of f, which we are allowed to query in order to construct a uniform approximating function. Under certain smoothness and variation
assumptions on the function g, and an arbitrary choice of the matrix A, we present in this paper
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