共查询到20条相似文献,搜索用时 31 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.
Fang Liping 《数学学报(英文版)》1998,14(1):139-144
Letf be a holomorphic self-map of the punctured plane ℂ*=ℂ\{0} with essentially singular points 0 and ∞. In this note, we discuss the setsI
0(f)={z ∈ ℂ*:f
n
(z) → 0,n → ∞} andI
∞(f)={z ∈ ℂ*:f
n
(z) → 0,n → ∞}. We try to find the relation betweenI
0(f),I
∞(t) andJ(f). It is proved that both the boundary ofI
0(f) and the boundary ofI
∞)f) equal toJ(f),I
0(f) ∩J(f) ≠ θ andI
∞(f) ∩J(f) ≠ θ. As a consequence of these results, we find bothI
0(f) andI
∞(f) are not doubly-bounded.
Supported by the National Natural Science Foundation of China 相似文献
3.
M. Filali 《Semigroup Forum》1994,48(1):163-168
LetG be a discrete abelian group,Ĝ the character group ofG, andl
∞(G)* the conjugate ofl
∞(G) equipped with an Arens product. In many cases, we can find unitary functionsf such that χf is almost convergent to zero for all χ∈Ĝ. Some of these functions are then used to produce elements μ∈l
∞(G)* such that γμ=0 whenever γ is an annihilator ofC
0(G). Regarded as Borel measures on βG, these elements satisfyxμ=0 for allx∈βG/G. They belong to the radical ofl
∞(G)*, and each of them generates a left ideal ofl
∞(G)* that contains no minimal left ideal. 相似文献
4.
Let f ∈ L
w
1
[−1, 1], let r
n,m(f) be the best rational L
w
1
-approximation for f with respect to real rational functions of degree at most n in the numerator and of degree at most m in the denominator, let m = m(n), and let lim
n → ∞ (n-m(n)) = ∞. In this case, we show that the counting measures of certain subsets of sign changes of f-r
n,m
(f) converge weakly to the equilibrium measure on [−1, 1] as n → ∞. Moreover, we prove estimates for discrepancy between these counting measures and the equilibrium measure.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 283–287, February, 2006. 相似文献
5.
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
6.
An Application of a Mountain Pass Theorem 总被引:3,自引:0,他引:3
We are concerned with the following Dirichlet problem:
−Δu(x) = f(x, u), x∈Ω, u∈H
1
0(Ω), (P)
where f(x, t) ∈C (×ℝ), f(x, t)/t is nondecreasing in t∈ℝ and tends to an L
∞-function q(x) uniformly in x∈Ω as t→ + ∞ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0,
0 > θF(x, s) ≤f(x, s)s, for all |s|≥M and x∈Ω, (AR)
is no longer true, where F(x, s) = ∫
s
0
f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming
(AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable
conditions on f(x, t) and q(x). Our methods also work for the case where f(x, t) is superlinear in t at infinity, i.e., q(x) ≡ +∞.
Received June 24, 1998, Accepted January 14, 2000. 相似文献
7.
Shu-Yu Hsu 《Mathematische Annalen》2006,334(1):153-197
Let a1,a2, . . . ,am ∈ ℝ2, 2≤f ∈ C([0,∞)), gi ∈ C([0,∞)) be such that 0≤gi(t)≤2 on [0,∞) ∀i=1, . . . ,m. For any p>1, we prove the existence and uniqueness of solutions of the equation ut=Δ(logu), u>0, in satisfying and logu(x,t)/log|x|→−f(t) as |x|→∞, logu(x,t)/log|x−ai|→−gi(t) as |x−ai|→0, uniformly on every compact subset of (0,T) for any i=1, . . . ,m under a mild assumption on u0 where We also obtain similar existence and uniqueness of solutions of the above equation in bounded smooth convex domains of ℝ2 with prescribed singularities at a finite number of points in the domain. 相似文献
8.
A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs. 相似文献
9.
In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” uf (·, T) is studied, where uf (x,t) is the solution of the initial boundary-value problem utt−Δu=0 in Ω×(0,T), u|t<0=0, u|∂Ω×(0,T)=f, and the (singular) control f runs over the class L2((0,T); H−m (∂Ω)) (m>0). The following result is established. Let ΩT={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝn (diam Ω<∞) filled with waves by a final instant of time t=T, let T*=inf{T : ΩT=Ω} be the time of filling the whole domain Ω. We introduce the notation Dm=Dom((−Δ)m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H2(Ω)∩H
0
1
(Ω);D−m=(Dm)′;D−m(ΩT)={y∈D−m:supp y ⋐ ΩT. If T<T., then the reachable set R
m
T
={ut(·, T): f ∈ L2((0,T), H−m (∂Ω))} (∀m>0), which is dense in D−m(ΩT), does not contain the class C
0
∞
(ΩT). Examples of a ∈ C
0
∞
, a ∈ R
m
T
, are presented.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21.
Translated by T. N. Surkova. 相似文献
10.
We obtain a generalization of the complete Perron effect whereby the characteristic exponents of all solutions change their
sign from negative for the linear approximation system to positive for a nonlinear system with perturbations of higher-order
smallness [Differ. Uravn., 2010, vol. 46, no. 10, pp. 1388–1402]. Namely, for arbitrary parameters λ
1 ≤ λ
2 < 0 and m > 1 and for arbitrary intervals [b
i
, d
i
) ⊂ [λ
i
,+∞), i = 1, 2, with boundaries d
1 ≤ b
2, we prove the existence of (i) a two-dimensional linear differential system with bounded coefficient matrix A(t) infinitely differentiable on the half-line t ≥ 1 and with characteristic exponents λ
1(A) = λ
1 ≤ λ
2(A) = λ
2 < 0; (ii) a perturbation f(t, y) of smallness order m > 1 infinitely differentiable with respect to time t > 1 and continuously differentiable with respect to y
1 and y
2, y = (y
1, y
2) ∈ R
2 such that all nontrivial solutions y(t, c), c ∈ R
2, of the nonlinear system .y = A(t)y + f(t, y), y ∈ R
2, t ≥ 1, are infinitely extendible to the right and have characteristic exponents λ[y] ∈ [b
1, d
1) for c
2 = 0 and λ[y] ∈ [b
2, d
2) for c
2 ≠ 0. 相似文献
11.
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
12.
A. N. Dyogtev 《Algebra and Logic》1996,35(2):80-85
Let A⊆N={0,1,2,...} and β be an n-ary Boolean function. We call A a β-implicatively selector (β-IS) set if there exists an
n-ary selector general recursive function f such that (∀x1,...,xn)(β(χ(x1),...,χ(xn))=1⟹f(x1,...,xn)∈A), where χ is the characteristic function of A. Let F(m), m≥1, be the family of all d
m+1
*
-IS sets, where
, F(0)=N, and F(∞) is the class of all subsets in N. The basic result of the article says that the family of all β-IS sets coincides with one
of F(m), m≥0, or F(∞), and, moreover, the inclusions F(0)⊂F(1)⊂...⊂F(∞) hold.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 145–153, March–April, 1996. 相似文献
13.
We give elementary proofs of the fact that the Loewner matrices
[\fracf(pi) - f (pj)pi-pj]{[\frac{f(p_i) - f (p_j)}{p_i-p_j}]} corresponding to the function f(t) = t
r
on (0, ∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0, ∞) the Loewner matrices corresponding
to an operator convex function on (−1, 1) need not be conditionally negative definite. 相似文献
14.
Baruch Solel 《Israel Journal of Mathematics》1988,62(1):63-89
LetM be a σ-finite von Neumann algebra andα be an action ofR onM. LetH
∞(α) be the associated analytic subalgebra; i.e.H
∞(α)={X ∈M: sp∞(X) [0, ∞]}. We prove that every σ-weakly closed subalgebra ofM that containsH
∞(α) isH
∞(γ) for some actionγ ofR onM. Also we show that (assumingZ(M)∩M
α = Ci)H
∞(α) is a maximal σ-weakly closed subalgebra ofM if and only if eitherH
∞(α)={A ∈M: (I−F)xF=0} for some projectionF ∈M, or sp(α)=Γ(α). 相似文献
15.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
16.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
17.
V. V. Arestov 《Ukrainian Mathematical Journal》2010,62(3):331-342
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment
[–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫–11 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞). 相似文献
18.
E. S. Dubtsov 《Siberian Mathematical Journal》2009,50(6):998-1006
Denote by Hol(B
n
) the space of all holomorphic functions in the unit ball B
n
of ℂ
n
, n ≥ 1. Given g ∈ Hol(B
m
) and a holomorphic mapping φ: B
m
→ B
n
, put C
φ
g
f = g · (f ∘ φ) for f ∈ Hol(B
n
). We characterize those g and φ for which C
φ
g
is a bounded (or compact) operator from the growth space A
−log(B
n
) or A
−β
(B
n
), β > 0, to the weighted Bergman space A
α
p
(B
m
), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators. 相似文献
19.
We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which
spreads through an epithelial basal layer modeled onI ⊂ Z
2. The solution of this problem is a familyp = (p
i(t)), where eachp
i(t)could be considered as an approximation to the probability that the cell situated ati is cancerous at timet. We prove that this problem has a unique solution, it is defined on [0, +∞[, and, for some relevant situations, limt→∞
P
i(t) = 1 for alli ∈ I. Moreover, we study the expected number of cancerous cells at timet. 相似文献
20.
本文利用文[2,3]的引理和算子L(a,c)f(z)的一些性质.结合Hadamard乘积,研究了算子L(a,c)f(z),获得了L(a,c)f(z)∈S*(β)和L(a,c)f(z)∈K(β)的充分条件,推广了文[2,3]的相关结论. 相似文献