共查询到20条相似文献,搜索用时 31 毫秒
1.
U. Goginava 《分析论及其应用》2007,23(3):255-265
In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β< 1/p,α,β> 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes. 相似文献
2.
Sergiy Maksymenko 《Annals of Global Analysis and Geometry》2006,29(3):241-285
Let M be a smooth compact surface, orientable or not, with boundary or without it, P either the real line ℝ
1 or the circle S
1, and D(M) the group of diffeomorphisms of M acting on C^∞(M, P) by the rule h⋅ f = f ∘ h
−1 for h ∊ D(M) and f ∊ C^∞ (M,P). Let f: M → P be an arbitrary Morse mapping, Σ
f
the set of critical points of f, D(M,Σ
f
) the subgroup of D(M) preserving Σ
f
, and S(f), S (f,Σ
f
), O(f), and O(f,Σ
f
) the stabilizers and the orbits of f with respect to D(M) and D(M,Σ
f
). In fact S(f) = S(f,Σ
f
).In this paper we calculate the homotopy types of S(f), O(f) and O(f,Σ
f
). It is proved that except for few cases the connected components of S(f) and O(f,Σ
f
) are contractible, π
k
O(f) = π
k
M for k ≥ 3, π2 O(f) = 0, and π1 O(f) is an extension of π1 D(M) ⊕ Z
k
(for some k ≥ 0) with a (finite) subgroup of the group of automorphisms of the Kronrod-Reeb graph of f.We also generalize the methods of F. Sergeraert to give conditions for a finite codimension orbit of a tame smooth action of a tame Lie group on a tame Fréchet manifold to be a tame Fréchet manifold itself. In particular, we obtain that O(f) and O(f, Σ
f
) are tame Fréchet manifolds.
Communicated by Peter Michor Vienna
Mathematics Subject Classifications (2000): 37C05, 57S05, 57R45. 相似文献
3.
Ana L. Bernardis Gladis Pradolini María Lorente María Silvina Riveros 《数学学报(英文版)》2010,26(8):1509-1518
For a Young function θ with 0 ≤α 〈 1, let Mα,θ be the fractional Orlicz maximal operator defined in the context of the spaces of homogeneous type (X, d, μ) by Mα,θf(x) = supx∈(B)α ||f||θ,B, where ||f||θ,B is the mean Luxemburg norm of f on a ball B. When α= 0 we simply denote it by Me. In this paper we prove that if Ф and ψare two Young functions, there exists a third Young function θ such that the composition Mα,ψ o MФ is pointwise equivalent to Mα,θ. As a consequence we prove that for some Young functions θ, if Mα,θf 〈∞a.e. and δ ∈(0,1) then (Mα,θf)δ is an A1-weight. 相似文献
4.
In this article we introduce the paranormed sequence spaces(f,Λ,△m,p),c0(f,Λ,△m,p) and ■∞(f,Λ,△m,p),associated with the multiplier sequence Λ =(λk),defined by a modulus function f.We study their different properties like solidness,symmetricity,completeness etc.and prove some inclusion results. 相似文献
5.
P. K. SAHO 《数学学报(英文版)》2005,21(5):1159-1166
In this paper, we determine the general solution of the functional equation f1 (2x + y) + f2(2x - y) = f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 : R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) = g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. 相似文献
6.
Our purpose here is to consider on a homogeneous tree two Pompeiutype problems which classically have been studied on the
plane and on other geometric manifolds. We obtain results which have remarkably the same flavor as classical theorems. Given
a homogeneous tree, letd(x, y) be the distance between verticesx andy, and letf be a function on the vertices. For each vertexx and nonnegative integern let Σ
n
f(x) be the sum Σ
d(x, y)=n
f(y) and letB
n
f(x)=Σ
d(x, y)≦n
f(y). The purpose is to study to what extent Σ
n
f andB
n
f determinef. Since these operators are linear, this is really the study of their kernels. It is easy to find nonzero examples for which
Σ
n
f orB
n
f vanish for one value ofn. What we do here is to study the problem for two values ofn, the 2-circle and the 2-disk problems (in the cases of Σ
n
andB
n respectively). We show for which pairs of values there can exist non-zero examples and we classify these examples. We employ
the combinatorial techniques useful for studying trees and free groups together with some number theory. 相似文献
7.
We discuss a technique for trying to find all rational points on curves of the form Y
2=f
3
X
6+f
2
X
4+f
1
X
2+f
0, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or
1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this
case, we shall derive an associated family of elliptic curves, defined over a number field ℚα. If each of these elliptic
curves has rank less than the degree of ℚα :
ℚ, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over ℚα) on the elliptic curves, for which x∈ℚ. This in turn allows us to find all ℚ-rational points on the original genus 2 curve. We apply this to give a solution to
a problem of Diophantus (where the sextic in X is irreducible over ℚ), which simplifies the recent solution of Wetherell. We also present two examples where the sextic
in X is reducible over ℚ.
Received: 27 November 1998 / Revised version: 4 June 1999 相似文献
8.
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
9.
Incompleteness and minimality of complex exponential system 总被引:3,自引:0,他引:3
Guan-tie DENG School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2007,50(10):1467-1476
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series. 相似文献
10.
We show a descent method for submodular function minimization based on an oracle for membership in base polyhedra. We assume
that for any submodular function f: ?→R on a distributive lattice ?⊆2
V
with ?,V∈? and f(?)=0 and for any vector x∈R
V
where V is a finite nonempty set, the membership oracle answers whether x belongs to the base polyhedron associated with f and that if the answer is NO, it also gives us a set Z∈? such that x(Z)>f(Z). Given a submodular function f, by invoking the membership oracle O(|V|2) times, the descent method finds a sequence of subsets Z
1,Z
2,···,Z
k
of V such that f(Z
1)>f(Z
2)>···>f(Z
k
)=min{f(Y) | Y∈?}, where k is O(|V|2). The method furnishes an alternative framework for submodular function minimization if combined with possible efficient
membership algorithms.
Received: September 9, 2001 / Accepted: October 15, 2001?Published online December 6, 2001 相似文献
11.
Gernot Greschonig 《Israel Journal of Mathematics》2005,147(1):245-267
LetT be a measure-preserving and ergodic transformation of a standard probability space (X,S, μ) and letf:X → SUT
d
(ℝ) be a Borel map into the group of unipotent upper triangulard ×d matrices. We modify an argument in [12] to obtain a sufficient condition for the recurrence of the random walk defined byf, in terms of the asymptotic behaviour of the distributions of the suitably scaled mapsf(n,x)=(fT
n−1·fT
n−2…fT·f). We give examples of recurrent cocycles with values in the continuous Heisenberg group H1(ℝ)=SUT3(ℝ), and we use a recurrent cocycle to construct an ergodic skew-product extension of an irrational rotation by the discrete
Heisenberg group H1(ℤ)=SUT3(ℤ).
The author was partially supported by the FWF research project P16004-MAT. 相似文献
12.
T. Akhobadze 《Acta Mathematica Hungarica》2002,97(3):223-256
Generalized Wiener classes are considered. For these classes the exact order of Fourier coefficients with respect to the trigonometric
system is established and the estimation of ‖S
n(·, f)-f(·)‖C
[0,2π] where S
n(·, f) are the Fourier partial sums, is given. In particular, a uniform convergence criterion for the Fourier trigonometric series
is obtained.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
13.
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
14.
V. A. Ustimenko 《Journal of Mathematical Sciences》2007,140(3):461-471
The paper is devoted to the study of a linguistic dynamical system of dimension n ≥ 2 over an arbitrary commutative ring K,
i.e., a family F of nonlinear polynomial maps f
α : K
n
→ K
n
depending on “time” α ∈ {K − 0} such that f
α
−1 = f
−αM, the relation f
α1 (x) = f
α2 (x) for some x ∈ Kn implies α1 = α2, and each map f
α has no invariant points. The neighborhood {f
α (υ)∣α ∈ K − {0}} of an element v determines the graph Γ(F) of the dynamical system on the vertex set Kn. We refer to F as a linguistic dynamical system of rank d ≥ 1 if for each string a = (α1, υ, α2), s ≤ d, where αi + αi+1 is a nonzero divisor for i = 1, υ, d − 1, the vertices υ
a = f
α1 × ⋯ × f
αs
(υ) in the graph are connected by a unique path. For each commutative ring K and each even integer n ≠= 0 mod 3, there is a family of linguistic dynamical systems Ln(K) of rank d ≥ 1/3n. Let L(n, K) be the graph of the dynamical system Ln(q). If K = Fq, the graphs L(n, Fq) form a new family of graphs of large girth. The projective limit L(K) of L(n, K), n → ∞, is well defined for each commutative
ring K; in the case of an integral domain K, the graph L(K) is a forest. If K has zero divisors, then the girth of K drops
to 4. We introduce some other families of graphs of large girth related to the dynamical systems Ln(q) in the case of even q. The dynamical systems and related graphs can be used for the development of symmetric or asymmetric
cryptographic algorithms. These graphs allow us to establish the best known upper bounds on the minimal order of regular graphs
without cycles of length 4n, with odd n ≥ 3. Bibliography: 42 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 214–234. 相似文献
15.
Denote by B
2σ,p
(1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [−σ, σ]. It is shown that a function in B
2σ,p
can be reconstructed in L
p(ℝ) by its sampling sequences {f (κπ / σ)}
κ∈ℤ and {f’ (κπ / σ)}
κ∈ℤ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L
p
r
(ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.
Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education under grant number
KM 200410009010 and by the Natural Science Foundation of China under grant number 10071006 相似文献
16.
Bogus?aw Bo?ek Wies?aw Solak Zbigniew Szyde?ko 《Central European Journal of Mathematics》2012,10(3):1172-1184
We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σ
i=1∞
f(i + 1/2) where f ∈ C
6 with its sixth derivative of constant sign on [m, ∞) and ∫
m
∞
f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature
rules with Gregory-Laplace end corrections, J. Comput. Appl. Math., 1991, 36(2), 251–253]. 相似文献
17.
E. Rips 《Israel Journal of Mathematics》1981,39(4):326-340
Letf
1, …,f
n be free generators of a free groupF. We consider the equation [z
1, …,z
n]ω. where ω and ω′ indicate the disposition of brackets in the higher commutators [z
1, …,z
n]ω and [f
1, …,f
n]ω. We give a necessary and sufficient condition on ω and ω′ for the existence of solutions of this equation. It is also shown
that for any solutionz
1=r1, …,z
z=r
n we have <r
1, …,r
n>=〈f
1, …f
n〉. 相似文献
18.
19.
Liliana Gabriela Gheorghe 《Annali di Matematica Pura ed Applicata》2001,180(2):203-210
We study membership to Schatten ideals S
E
, associated with a monotone Riesz–Fischer space E, for the Hankel operators H
f
defined on the Hardy space H
2(∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H
f
∈S
E
if and only if f∈B
E
, the Besov space associated with a monotone Riesz–Fischer space E(dλ) over the measure space (D,dλ) and the main tool is the interpolation of operators.
Received: December 17, 1999; in final form: September 25, 2000?Published online: July 13, 2001 相似文献
20.
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