共查询到20条相似文献,搜索用时 656 毫秒
1.
Toshiyuki Sugawa 《Monatshefte für Mathematik》2003,50(7):61-68
The inner radius of univalence of a domain D with Poincaré density ρ
D
is the possible largest number σ such that the condition ∥ S
f
∥
D
= sup
w∈ D
ρ
D
(w)
−2∥ S
f
(z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S
f
is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms
of the order α. 相似文献
2.
Jiří Matoušek 《Israel Journal of Mathematics》1999,114(1):221-237
We investigate the minimum value ofD =D(n) such that anyn-point tree metric space (T, ρ) can beD-embedded into a given Banach space (X, ∥·∥); that is, there exists a mappingf :T →X with 1/D ρ(x,y) ≤ ∥f(x) −f(y)∥ ≤ρ(x,y) for anyx,y εT. Bourgain showed thatD(n) grows to infinity for any superreflexiveX (and this characterized super-reflexivity), and forX =ℓ
p, 1 <p < ∞, he proved a quantitative lower bound of const·(log logn)min(1/2,1/p). We give another, completely elementary proof of this lower bound, and we prove that it is tight (up to the value of the
constant). In particular, we show that anyn-point tree metric space can beD-embedded into a Euclidean space, with no restriction on the dimension, withD =O(√log logn).
This paper contains results from my thesis [Mat89] from 1989. Since the subject of bi-Lipschitz embeddings is becoming increasingly
popular, in 1997 I finally decided to publish this English version.
Supported by Czech Republic Grant GAČR 0194 and by Charles University grants No. 193, 194. 相似文献
3.
V. D. Derech 《Ukrainian Mathematical Journal》2012,63(9):1390-1399
For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms
are permutable. 相似文献
4.
Christiane Kraus 《Constructive Approximation》2011,33(2):191-217
The aim of this paper is to extend the classical maximal convergence theory of Bernstein and Walsh for holomorphic functions
in the complex plane to real analytic functions in ℝ
N
. In particular, we investigate the polynomial approximation behavior for functions F:L→ℂ, L={(Re z,Im z):z∈K}, of the structure F=g[`(h)]F=g\overline{h}, where g and h are holomorphic in a neighborhood of a compact set K⊂ℂ
N
. To this end the maximal convergence number ρ(S
c
,f) for continuous functions f defined on a compact set S
c
⊂ℂ
N
is connected to a maximal convergence number ρ(S
r
,F) for continuous functions F defined on a compact set S
r
⊂ℝ
N
. We prove that ρ(L,F)=min {ρ(K,h)),ρ(K,g)} for functions F=g[`(h)]F=g\overline{h} if K is either a closed Euclidean ball or a closed polydisc. Furthermore, we show that min {ρ(K,h)),ρ(K,g)}≤ρ(L,F) if K is regular in the sense of pluripotential theory and equality does not hold in general. Our results are based on the theory
of the pluricomplex Green’s function with pole at infinity and Lundin’s formula for Siciak’s extremal function Φ. A properly chosen transformation of Joukowski type plays an important role. 相似文献
5.
A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth,
distortion, curvature and covering theorems for B∞(α).
Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation.
Research supported in part by a National Science Foundation grant. 相似文献
6.
Andrea Sambusetti 《manuscripta mathematica》1999,99(4):541-560
We prove that MinEnt (Y) ∥Y∥ = MinEnt(X) ∥X∥, for manifolds Y whose fundamental group is a subexponential extension of the fundamental group of some negatively curved, locally symmetric
manifold X. This is a particular case of a more general result holding for an arbitrary representation ρ : π1 (Y) →π1 (X), which relates the minimal entropy and the simplicial volume of X to some invariants of the couple (Y, ker (ρ)). Then, we discuss some applications to the minimal volume problem and to Einstein metrics.
Received: 23 December 1998 相似文献
7.
H. Wang 《Lithuanian Mathematical Journal》2010,50(4):474-488
Let c
n
be the Fourier coefficients of L(sym
m
f, s), and Δρ(x; sym
m
f) be the error term in the asymptotic formula for ∑
n≪x
c
n
. In this paper, we study the Riesz means of Δρ(x; sym
m
f) and obtain a truncated Voronoi-type formula under the hypothesis Nice(m, f). 相似文献
8.
Ana Bela CRUZEIRO Xi Cheng ZHANG 《数学学报(英文版)》2006,22(1):101-104
For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2(Ttf)‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2((I- L) ^-α) is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖(I - L)^αf‖p,Cq,α(I-L)^(1-α)‖Df‖q+‖f‖q, where D is the Malliavin gradient ([2]) and L the Ornstein-Uhlenbeck operator. 相似文献
9.
Given a specification linear operatorS, we want to test an implementation linear operatorA and determine whether it conforms to the specification operator according to an error criterion. In an earlier paper [3],
we studied a worst case error in which we test whether the error is no more than a given bound ε>0 for all elements in a given
setF, i.e., sup
fεf∥Sf—Af∥≤ε. In this work, we study the average error instead, i. e., ∫
F
∥Sf-Af∥2μ(df)ɛ≤2, where μ is a probability measure onF. We assume that an upper boundK on the norm of the difference ofS andA is given a priori. It turns out that any finite number of tests is in general inconclusive with the average error. Therefore,
as in the worst case, we allow a relaxation parameter α>0 and test for weak conformance with an error bound (1+α)ε. Then a
finite number of tests from an arbitrary orthogonal complete sequence is conclusive. Furthermore, the eigenvectors of the
covariance operatorC
μ of the probability measure μ provide an almost optimal test sequence. This implies that the test set isuniversal; it only depends on the set of valid inputsF and the measure μ, and is independent ofS, A, and the other parameters of the problem. However, the minimal number of tests does depend on all the parameters of the testing
problem, i.e., ε, α,K, and the eigenvalues ofC
μ. In contrast to the worst case setting, it also depends on the dimensiond of the range space ofS andA.
This work was done while consulting at Bell Laboratories, and is partially supported by the National Science Foundation and
the Air Force Office of Scientific Research. 相似文献
10.
Bernard Pinchuk 《Israel Journal of Mathematics》1971,10(1):6-16
Classes of functionsU
k, which generalize starlike functions in the same manner that the classV
k of functions with boundary rotation bounded bykπ generalizes convex functions, are defined. The radius of univalence and starlikeness is determined. The behavior off
α(z) = ∫
0
z
[f'(t)]α
dt is determined for various classes of functions. It is shown that the image of |z|<1 underV
kfunctions contains the disc of radius 1/k centered at the origin, andV
k functions are continuous in |z|≦1 with the exception of at most [k/2+1] points on |z|=1. 相似文献
11.
Let S′ be the class of tempered distributions. For ƒ ∈ S′ we denote by J
−α
ƒ the Bessel potential of ƒ of order α. We prove that if J
−α
ƒ ∈ BMO, then for any λ ∈ (0, 1), J
−α
(f)λ ∈ BMO, where (f)λ = λ−n
f(φ(λ−1)), φ ∈ S. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order
α > 0 belongs to the VMO space. 相似文献
12.
Rumi Shindo 《Central European Journal of Mathematics》2010,8(1):135-147
Let A and B be uniform algebras. Suppose that α ≠ 0 and A
1 ⊂ A. Let ρ, τ: A
1 → A and S, T: A
1 → B be mappings. Suppose that ρ(A
1), τ(A
1) and S(A
1), T(A
1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A
1, S(e
1)−1 ∈ S(A
1) and S(e
1) ∈ T(A
1) for some e
1 ∈ A
1 with ρ(e
1) = 1, then there exists a real-algebra isomorphism $
\tilde S
$
\tilde S
: A → B such that $
\tilde S
$
\tilde S
(ρ(f)) = S(e
1)−1
S(f) for every f ∈ A
1. We also give some applications of this result. 相似文献
13.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
14.
Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation |〈f(x), f(y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmielinski by proving a theorem: LetD
n be a suitable subset of ℝn. If a function f:D
n → ℝn satisfies the inequality ∥〈f(x), f(y)〉| |〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ D
n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D
n. 相似文献
15.
We derive a Carleson type estimate for positive solutions of non-divergence second order elliptic equations Lu = a
ij
D
ij
u + b
i
D
i
u = 0 in a bounded domain Ω ⊂ ℝ
n
. We assume that b
i
∈ L
n
(Ω) and Ω is a twisted H?lder domain of order α ∈ (1/2, 1] which satisfies a weak regularity condition. We also provide an example which shows that the main result fails
in general if α ∈ (0, 1/2]. Bibliography: 18 titles. 相似文献
16.
Osamu Hatori Takeshi Miura Rumi Shindo Hiroyuki Takagi 《Rendiconti del Circolo Matematico di Palermo》2010,59(2):161-183
Let $
A
$
A
and ℬ be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: $
A
$
A
→ ℬ with S(1)=T(1)= 1 and α ∈ ℂ \ {0} satisfy r(S(a)T(b) − α)= r(ab− α) for all a,b ∈ $
A
$
A
, then S=T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σ
π
(S(p)T(q)) ⊂ σ
π
(ρ(p) τ(q)) for all p,q ∈ I, where σ
π
(f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions “enough”. There exists a homeomorphism ϕ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(ϕ(y)) and T(p)(y)= τ(p)(ϕ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A. 相似文献
17.
We consider a mechanical model in the plane, consisting of a vertical rod, subject to a constant horizontal force f and to elastic collisions with the particles of a free gas which is “horizontally” in equilibrium at some inverse temperature
β. In a previous paper we proved that, in the appropriate space and time scaling, the motion of the rod is described as a drift
term plus a diffusion term. In this paper we prove that the drift d(f) and the diffusivity σ
2
(f) are continuous functions of f, and moreover that the Einstein relation holds, i.e.,
lim
f → 0
d(f)f = β2 σ
2
(0) .
Received: 26 January 1996 / In revised form: 2 October 1996 相似文献
18.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
19.
We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [Combinatorica, 1995]. For
a graph G, let dim(G) be the smallest d such that G occurs as a (not necessarily induced) subgraph of ℤ∞
d
, the infinite graph with vertex set ℤ
d
and an edge (u, v) whenever ∥u − v∥∞ = 1. The growth rate of G, denoted ρ
G
, is the minimum ρ such that every ball of radius r > 1 in G contains at most r
ρ
vertices. By simple volume arguments, dim(G) = Ω(ρ
G
). Levin conjectured that this lower bound is tight, i.e., that dim(G) = O(ρ
G
) for every graph G.
Previously, it was unknown whether dim(G) could be bounded above by any function of ρ
G
. We show that a weaker form of Levin’s conjecture holds by proving that dim(G) = O(ρ
G
log ρ
G
) for any graph G. We disprove, however, the specific bound of the conjecture and show that our upper bound is tight by exhibiting graphs for
which dim(G) = Ω(ρ
G
log ρ
G
). For several special families of graphs (e.g., planar graphs), we salvage the strong form, showing that dim(G) = O(ρ
G
). Our results extend to a variant of the conjecture for finite-dimensional Euclidean spaces posed by Linial and independently
by Benjamini and Schramm.
Supported by NSF grant CCR-0121555 and by an NSF Graduate Research Fellowship. 相似文献
20.
For the mappings
f:D ? D¢, D, D¢ ì \mathbbRn f:D \to D',\,\,D,\,\,D' \subset {\mathbb{R}^n}
, n ≥ 2, satisfying certain geometric conditions in the fixed domain D, we have proved estimates of the form K
I
(x, f) ≤ Q(x) almost everywhere, where K
I
(x, f) is the inner dilatation of f at a point x, and Q(x) is a fixed real-valued function responsible for the “control” over a distortion of the families of curves in D at a mapping f. 相似文献