共查询到20条相似文献,搜索用时 859 毫秒
1.
We consider complex-valued functions f ∈ L 1 (R+2),where R +:= [0,∞),and prove sufficient conditions under which the double sine Fourier transform f ss and the double cosine Fourier transform f cc belong to one of the two-dimensional Lipschitz classes Lip(α,β) for some 0 α,β≤ 1;or to one of the Zygmund classes Zyg(α,β) for some 0 α,β≤ 2.These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1 (R+2). 相似文献
2.
We investigate the growth and the distribution of zeros of rational uniform approximations with numerator degree ≤n and denominator degree ≤m
n
for meromorphic functions f on a compact set E of ℂ where m
n
=o(n/log n) as n→∞. We obtain a Jentzsch–Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of
the maximal Green domain E
ρ(f) of meromorphy of f if f has a singularity of multivalued character on the boundary of E
ρ(f). The paper extends results for polynomial approximation and rational approximation with fixed degree of the denominator.
As applications, Padé approximation and real rational best approximants are considered. 相似文献
3.
V. D. Zalizko 《Ukrainian Mathematical Journal》2007,59(1):28-44
The Jackson inequality
relates the value of the best uniform approximation E
n
(f) of a continuous 2π-periodic function f: ℝ → ℝ by trigonometric polynomials of degree ≤ n − 1 to its third modulus of continuity ω
3(f, t). In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity
on [−π, π) only at every point of a fixed finite set consisting of an even number of points are approximated by polynomials
coconvex to them.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 29–43, January, 2007. 相似文献
4.
The Grunsky coefficient inequalities play a crucial role in various problems and are intrinsically connected with the integrable
holomorphic quadratic differentials having only zeros of even order. For the functions with quasi-conformal extensions, the
Grunsky constant ℵ(f) and the extremal dilatationk(f) are related by ℵ(f)≤k(f). In 1985, Jürgen Moser conjectured that any univalent functionf(z)=z+b
0+b
1
z
−1+… on Δ*={|z|>1} can be approximated locally uniformly by functions with ℵ(f)<k(f). In this paper, we prove a theorem confirming Moser’s conjecture, which sheds new light on the features of Grunsky coefficients.
In memory of Jürgen Moser
The research was supported by the RiP program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach. 相似文献
5.
For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property. 相似文献
6.
N. V. Taranenko 《Ukrainian Mathematical Journal》2000,52(2):294-304
We consider a family of completely additive functions βq(n) defined on the set of natural numbers. We find an asymptotic expression for the summation function Σ
n≤x
β
q
(n study its distribution on short intervals. 相似文献
7.
Norbert Steinmetz 《Journal d'Analyse Mathématique》2012,117(1):347-364
We discuss families of meromorphic functions f h obtained from single functions f by the re-scaling process f h (z) = h −α f (h + h −β z), generalising Yosida’s process f h (z) = f (h + z). The main objective is to obtain information about the value distribution of the generating functions f themselves. Among the most prominent (generalised) Yosida functions are the elliptic functions and also some first, second and fourth Painlevé transcendents. The Yosida class A 0 contains all limit functions of generalised Yosida functions-the Yosida class is universal. 相似文献
8.
Szilvia Szilágyi 《Order》2008,25(4):321-333
We present a characterization of the maximal compatible extensions of a given compatible partial order ≤
r
on a unary algebra (A,f ). These extensions can be constructed by using the compatible linear extensions of ≤
r*, where (A*,f*) is the so called contracted quotient algebra of (A,f) and the compatible partial order ≤
r* on (A*,f*) is naturally induced by ≤
r
. Using this characterization, we determine the intersection of the maximal compatible extensions of ≤
r
.
相似文献
9.
For β > 0 and an integer r ≥ 2, denote by [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r those 2π-periodic, real-valued functions f on ℝ, which are analytic in S
β
:= {z ∈ ℂ: |Im z| < β} and satisfy the restriction |f
(r)(z)|≤1, z ∈ S
β
. The optimal quadrature formulae about information composed of the values of a function and its kth (k = 1, ..., r − 1) derivatives on free knots for the classes [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r are obtained, and the error estimates of the optimal quadrature formulae are exactly determined. 相似文献
10.
A. Yu. Solynin 《Journal of Mathematical Sciences》1990,52(3):3115-3123
By the method of the moduli of families of curves one solves some extremal problems in the family of pairs {f1, f2} of functions f1(z)=αz + ..., f2(z)=βz-1 + β0 +β1z+..., with real coefficients, univalent, regular, resp. meromorphic in the circle Δ={∥z∥<1} and mapping onto nonoverlapping
domains. As a special case the solution of a problem, posed by V. M. Miklyukov in Sib. Mat. Zh., Vol. 18, 1977, No. 5, pp.
1111–1124, is obtained.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 159–169, 1987. 相似文献
11.
M. -B. A. Babaev 《Mathematical Notes》1997,62(1):15-29
We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions
of fewer variables. The order of approximation of Sobolev classesW
q
r
by bilinear forms inL
p
for 2≤q≤p≤∞ is found.
Translated by N. K. Kulman
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997. 相似文献
12.
F. Redig 《Bulletin of the Brazilian Mathematical Society》2002,33(3):427-446
We consider one-dimensional Gibbs measures on spin configurations σ ∈ {–1,+1}ℤ. For N ∈ ℕ let l
N
denote the length of the longest interval of consecutive spins of the same kind in the interval [0,N]. We show that the distribution of a suitable continuous modification l
c
(N) of l
N
converges to the Gumbel distribution, i.e., for some α, β ∈ (0, ∞) and γ ∈ ℝ,
lim
N
→∞ ℙ(l
c
(N) ≤ α log N + βx + γ) = e
–e
–x
.
Received: 2 September 2002 相似文献
13.
Jean-Philippe Furter 《manuscripta mathematica》1999,98(2):183-193
For a polynomial automorphism f of ?2
ℂ, we set τ = deg f
2)/(deg f). We prove that τ≤ 1 if and only if f is triangularizable. In this situation, we show (by using a deep result from number theory known as the theorem of Skolem–Mahler–Lech)
that the sequence (deg f
n
)
n
∈ℕ is periodic for large n. In the opposite case, we prove that τ is an integer (τ≥ 2) and that the sequence (deg f
n
)
n
∈ℕ is a geometric progression of ratio τ. In particular, if f is any automorphism, we obtain the rationality of the formal series .
Received: 1 December 1997 相似文献
14.
HaoZHAO GuiZhenLIU XiaoXiaYAN 《数学学报(英文版)》2005,21(2):413-422
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integervalued functions defined on V(G) such that 2k - 2 ≤g(x)≤f(x) for all x∈V(G). Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg m-1,mf-m 1)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions. 相似文献
15.
We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove some direct
approximation theorems for functions f such that w
σ
f ∈ L
p
(R), where 1 ≤ p ≤ ∞ and w
σ
(x) = exp(−σx
2), σ > 0. 相似文献
16.
Given the f-vector f = (f0, f1, . . .) of a Cohen–Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δf with f(Δf) = f such that, for any Cohen–Macaulay simplicial complex Δ with f(Δ) = f, one has
for all i and j, where f(Δ) is the f-vector of Δ and where β
ij
(I
Δ) are graded Betti numbers of the Stanley–Reisner ideal I
Δ of Δ.
The first author is supported by JSPS Research Fellowships for Young Scientists.
Received: 23 January 2006 相似文献
17.
We consider an unknown response function f defined on Δ = [0, 1]
d
, 1 ≤ d ≤ ∞, taken at n random uniform design points and observed with Gaussian noise of known variance. Given a positive sequence r
n
→ 0 as n → ∞ and a known function f
0 ∈ L
2(Δ), we propose, under general conditions, a unified framework for goodness-of-fit testing the null hypothesis H
0: f = f
0 against the alternative H
1: f ∈ $
\mathcal{F}
$
\mathcal{F}
, ∥f − f
0∥ ≥ r
n
, where $
\mathcal{F}
$
\mathcal{F}
is an ellipsoid in the Hilbert space L
2(Δ) with respect to the tensor product Fourier basis and ∥ · ∥ is the norm in L
2(Δ). We obtain both rate and sharp asymptotics for the error probabilities in the minimax setup. The derived tests are inherently
non-adaptive.
Several illustrative examples are presented. In particular, we consider functions belonging to ellipsoids arising from the
well-known multidimensional Sobolev and tensor product Sobolev norms as well as from the less-known Sloan-Woźniakowski norm
and a norm constructed from multivariable analytic functions on the complex strip. 相似文献
18.
Robert Kantrowitz Michael M. Neumann 《Rendiconti del Circolo Matematico di Palermo》2005,54(2):291-302
Ifh denotes the product of finitely many concave non-negative functions on a compact interval [a, b], then it is shown that there exist pointsα andβ witha≤α≤β≤b such thath is strictly increasing on [α, α), constant on (α, β), and strictly decreasing on (β, b]. This structure theorem leads to an extension of several classical optimization results for concave functions on convex
sets to the case of products of concave functions. 相似文献
19.
Ming Ju LIU Shan Zhen LU 《数学学报(英文版)》2007,23(1):7-16
In this paper, the authors study some properties of Littlewood-Paley g-functions gψ(f),Lusin area functions Sψ,α(f) and Littlewood-Paley gψ^*,λ(f) functions defined on H^n, where α,λ 〉 0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on R^n. 相似文献
20.
In this paper the closed convex hulls of the compact familiesC
β(p), of multivalently close to convex functions of order β andV
0
k
(p), of multivalent functions of bounded boundary rotation, have been determined, respectively for β≥1 andk≥2(p+1)/p. Extreme points of these convex hulls are partially characterised. For a fixed pointz
0∈D={z:|z|<1}, a new familyC
β(p, z0) is defined through Montel normalisation and its closed convex hull is also foud. Sharp coefficient estimates for functions
subordinate to or majorised by some function inC
β(p) orC'
β(p) are discussed for β>0. It is shown that iff is subordinate to some function inC
β(p) then each Taylor coefficient off is dominated by the corresponding coefficient of the function
. 相似文献