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1.
拟圆周的两个几何性质 总被引:3,自引:0,他引:3
§1 IntroductionLetΓbe a Jordan curve of R2 and f∶R2→R2 be a k-quasiconformal mapping,where1≤k<+∞.Γis called a quasicirlce ifΓis the image of the unit circle B2 under f.It is well-known that quasicircles play a very important role in quasiconformalmapping theory,complex dynamics,Fuchsian groups,Teichmuller space theory and lowdimensional topology,( see[1—5] etc.)In1 963 ,Ahlfors obtained the three-point property of quasidisks[6] .Later,Gehring[7] ,Osgood[8] ,Krzyz[9] ,Ch… 相似文献
2.
O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1733-1748
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
It is proved that for large K,
where ε > 0 is arbitrary. For f ∈ Sk(Γ)+, let L(s, sym
2 f) denote the symmetric square L-function. It is proved that as k → ∞ the frequence
converges to a distribution function G(x) at every point of continuity of the latter, and for the corresponding characteristic
function an explicit expression is obtained. Bibliography: 17 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 221–246. 相似文献
3.
S. S. Podkorytov 《Journal of Mathematical Sciences》2007,140(4):589-610
Fix an m ∈ ℕ, m ≥ 2. Let Y be a simply connected pointed CW-complex, and let B be a finite set of continuous mappings a: Sm → Y respecting the distinguished points. Let Γ(a) ⊂ Sm × Y be the graph of a, and we denote by [a] ∈ πm(Y) the homotopy class of a. Then for some r ∈ ℕ depending on m only, there exist a finite set E ⊂ Sm × Y and a mapping k: E(r) = {F ⊂ E: |F| ≤ r} → πm(Y) such that for each a ∈ B we have
. Bibliography: 5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 159–194. 相似文献
4.
Klaus Schmidt 《Israel Journal of Mathematics》1982,41(1-2):151-153
LetG be a locally compact second countable abelian group, (X, μ) aσ-finite Lebesgue space, and (g, x) →gx a non-singular, properly ergodic action ofG on (X, μ). Let furthermore Γ be the character group ofG and let Sp(G, X) ⊂ Γ denote theL
∞-spectrum ofG on (X, μ). It has been shown in [5] that Sp(G, X) is a Borel subgroup of Γ and thatσ (Sp(G, X))<1 for every probability measureσ on Γ with lim supg→∞Re
(g)<1, where
is the Fourier transform ofσ. In this note we prove the following converse: ifσ is a probability measure on Γ with lim supg→∞Re
(g)<1 (g)=1 then there exists a non-singular, properly ergodic action ofG on (X, μ) withσ(Sp(G, X))=1. 相似文献
5.
S. V. Kolesnikov 《Mathematical Notes》1998,63(1):50-54
This work presents two remarks on the structure of singular boundary sets of functions analytic in the unit diskD: |z|<1. The first remark concerns the conversion of the Plessner theorem. We prove that three pairwise disjoint subsetsE
1,E
2, andE
3 of the unit circle Γ: |z|=1,
= Γ, are the setsI(ƒ) of all Plessner points,F(ƒ) of all Fatou points, andE(ƒ) of all exceptional boundary points, respectively, for a function ƒ holomorphic inD if and only ifE
1 is aG
δ-set andE
3 is a
-set of linear measure zero. In the second part of the paper it is shown that for any
-subsetE of the unit circle Γ with a zero logarithmic capacity there exists a one-sheeted function onD whose angular limits do not exist at the points ofE and do exist at all the other points of Γ.
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 56–61, January, 1998. 相似文献
6.
D. M. Smirnov 《Algebra and Logic》2005,44(5):348-352
We deal with varieties with one basic operation f(x1,...,xn) and one defining identity f(x1,..., xn) = f(xπ(1),...,xπ(n)), where π is a permutation whose cyclic set consists of distinct primes p1,...,pr, with the sum p1+...+pr = n. Their interpretability types, together with the greatest element 1 in a lattice
int, are said to be arithmetic. It is proved that the arithmetic types constitute a distributive lattice
ar, which is dual to a lattice Sub
fΠ of finite subsets of the set Π of all primes. It is shown that for n ⩾ 2, the poset
ar(
n) of arithmetic types defined by permutations in
n, for n fixed, is a lattice iff n = 2, 3, 4, 6, 8, 9, 11.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005. 相似文献
7.
Given a lattice Γ in a locally compact group G and a closed subgroup H of G, one has a natural action of Γ on the homogeneous space V = H\ G. For an increasing family of finite subsets {Γ
T
: T > 0}, a dense orbit υ· Γ, υ∈V and compactly supported function φ on V, we consider the sums
. Understanding the asymptotic behavior of S
φ,υ
(T) is a delicate problem which has only been considered for certain very special choices of H,G and {Γ
T
}. We develop a general abstract approach to the problem, and apply it to the case when G is a Lie group and either H or G is semisimple. When G is a group of matrices equipped with a norm, we have
where G
T
= {g ∈G: ||g|| < T} and Γ
T
= G
T
∩ Γ. We also show that the asymptotics of S
φ, υ
(T) is governed by
where ν is an explicit limiting density depending on the choice of υ and || · ||.
Submitted: March 2005 Revision: April 2006 Accepted: June 2006 相似文献
8.
Let N be a compact simply connected smooth Riemannian manifold and, for p ∈ {2,3,...}, W
1,p
(R
p+1, N) be the Sobolev space of measurable maps from R
p+1 into N whose gradients are in L
p
. The restriction of u to almost every p-dimensional sphere S in R
p+1 is in W
1,p
(S, N) and defines an homotopy class in π
p
(N) (White 1988). Evaluating a fixed element z of Hom(π
p
(N), R) on this homotopy class thus gives a real number Φ
z,u
(S). The main result of the paper is that any W
1,p
-weakly convergent limit u of a sequence of smooth maps in C
∞(R
p+1, N), Φ
z,u
has a rectifiable Poincaré dual
. Here Γ is a a countable union of C
1 curves in R
p+1 with Hausdorff -measurable orientation and density function θ: Γ→R. The intersection number between and S evaluates Φ
z,u
(S), for almost every p-sphere S. Moreover, we exhibit a non-negative integer n
z
, depending only on homotopy operation z, such that even though the mass may be infinite. We also provide cases of N, p and z for which this rational power p/(p + n
z
) is optimal. The construction of this Poincaré dual is based on 1-dimensional “bubbling” described by the notion of “scans”
which was introduced in Hardt and Rivière (2003). We also describe how to generalize these results to R
m
for any m ⩾ p + 1, in which case the bubbling is described by an (m–p)-rectifiable set with orientation and density function determined by restrictions of the mappings to almost every oriented
Euclidean p-sphere. 相似文献
9.
V. V. Bakun 《Ukrainian Mathematical Journal》2000,52(2):173-182
We prove that the functionals of a d-dimensional Brownian process are Hida distributions, i.e., generalized Wiener functionals. Here, δΓ(·) is a generalization of the δ-function constructed on a bounded closed smooth surface Γ⊂R
d
, k≥1 and acting on finite continuous functions φ(·) in R
d according to the rule where ι(·) is a surface measure on Γ. 相似文献
10.
Summary Let
a plane angle of opening α∈(π, 2π). LetP
D andP
N the Dirichlet and Neumann problems associated to the Poisson equation in
. ForP
D andP
N it is proved non existence of solution in L
p
(
) whenp=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated toP
D andP
N are not-closed in L
p
(
) forp=2/(1±π/α).
Sunto Sia } un angolo piano di apertura α∈(π, 2π). SianoP D eP N i problemi di Dirichlet e di Neumann associati all'equazione di Poisson in . PerP D eP N si prova non esistenza di soluzioni in L p ( ) quandop=2/(1±π/α). Vale a dire i ranges degli operatori ellittici naturalmente associati aP D eP N sono non-chiusi in π--AgBrα K L p ( ) perp=2/(1±π/α).相似文献
11.
We consider the Riemann–Hilbert problem in the following setting: find a function whose boundary values ϕ+(t) satisfy the condition a.e. on Γ. Here D is a simply connected domain bounded by a simple closed curve Γ, and K
p( · )(D;ω) is the set of functions ϕ(z) representable in the form , where ω(z) is a weight function and (K
Γφ
)(z) is a Cauchy type integral whose density φ is integrable with a variable exponent p(t). It is assumed that Γ is a piecewise-Lyapunov curve without zero angles, ω(z) is an arbitrary power function and p(t) satisfies the Log-H?lder condition. The solvability conditions are established and solutions are constructed. These solutions
largely depend on the coefficients a, b, c, the weight ω, on the values of p(t) at the angular points of Γ and on the values of angles at these points.
Submitted: May 13, 2007. Revised: August 8, 2007 and August 28, 2007. Accepted: November 8, 2007. 相似文献
12.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
13.
E. Amar 《Journal of Geometric Analysis》1991,1(4):291-305
We show that if f1, f2 are bounded holomorphic functions in the unit ball
of ℂn such that
, |f1(z)|2 + |f2(z)2|2 ≥ δ2 >; 0, then any functionh in the Hardy space
,p < +∞ can be decomposed ash = f1h1
+ f2h2 with
. The Corona theorem in
would be the same result withp = +∞ and this question is still open forn ≳-2, but the preceding result goes in this direction. 相似文献
14.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
15.
We study the boundary-value problemu
tt
-u
xx
=g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of, and-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods, and which characterize the classes of π-, 2π -, and 4π-periodic functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 281–284, February, 1999. 相似文献
16.
Take a linear ordinary differential operator $\mathfrak{d}\left( z \right) = \sum\nolimits_{i = 1}^k {Q_i \left( z \right)\frac{{d^i }}
{{dz^i }}}$\mathfrak{d}\left( z \right) = \sum\nolimits_{i = 1}^k {Q_i \left( z \right)\frac{{d^i }}
{{dz^i }}} with polynomial coefficients and set r = max
i=1,…,k(deg Q
i
(z) − i). If d(z) satisfies the conditions: (i) r ≥ 0 and (ii) deg Q
k
(z) = k + r, we call it a non-degenerate higher Lamé operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [13] the study of the following multiparameter spectral problem: for each positive integer n find polynomials V (z) of degree at most r such that the equation
\mathfrakd( z )S( z ) + V( z )S( z ) = 0\mathfrak{d}\left( z \right)S\left( z \right) + V\left( z \right)S\left( z \right) = 0 相似文献
17.
Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1∫
D
∇h(z)⋅∇h(z)dz, and a constant 0≤γ<2. The Liouville quantum gravity measure on D is the weak limit as ε→0 of the measures
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