共查询到20条相似文献,搜索用时 46 毫秒
1.
Ferenc Móricz 《Acta Mathematica Hungarica》2012,134(3):356-368
We consider complex-valued functions f∈L
1(ℝ+), where ℝ+:=[0,∞), and prove sufficient conditions under which the sine Fourier transform [^(f)]s\hat{f}_{s} and the cosine Fourier transform [^(f)]c\hat{f}_{c} belong to one of the Lipschitz classes Lip (α) and lip (α) for some 0<α≦1, or to one of the Zygmund classes Zyg (α) and zyg (α) for some 0<α≦2. These sufficient conditions are best possible in the sense that they are also necessary if f(x)≧0 almost everywhere. 相似文献
2.
In this paper we study the existence and uniqueness of solutions of the Beltrami equationf
-z
(z) =Μ(z)f
z
(z), whereΜ(z) is a measurable function defined almost everywhere in a plane domain ‡ with ‖ΜΜ∞ = 1-Here the partialsf
z
andf
z
of a complex valued functionf
z
exist almost everywhere. In case ‖Μ‖∞ ≤9 < 1, it is well-known that homeomorphic solutions of the Beltrami equation are quasiconformal
mappings. In case ‖Μ‖∞= 1, much less is known. We give sufficient conditions onΜ(z) which imply the existence of a homeomorphic solution of the Beltrami equation, which isACL and whose partial derivativesf
z
andf
z
are locally inL
q
for anyq < 2. We also give uniqueness results. The conditions we consider improve already known results. 相似文献
3.
Bálint Farkas 《Czechoslovak Mathematical Journal》2011,61(2):309-322
For a given bi-continuous semigroup (T(t))
t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ(X°,X). We give the following application: For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(Ω) of bounded Baire measures
(endowed with the weak*-topology). We show that bi-continuous semigroups on M(Ω) are precisely those that are adjoints of
bi-continuous semigroups on Cb(Ω). We also prove that the class of bi-continuous semigroups on Cb(ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict
topology. In general, if is not a Polish space this is not the case. 相似文献
4.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1996,48(3):460-466
We prove that, for every sequence (a
k) of complex numbers satisfying the conditions Σ(1/|a
k
|) < ∞ and |a
k+1| − |a
k
| ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such thatf(z) = Π(1 −z/|a
k
|) is an entire function of finitel-index. 相似文献
5.
F. Luca I. E. Shparlinski 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):143-156
Let (un)n≥0 be a non-degenerate linear recurrence sequence of integers. We show that the set of positive integersn such that either ω)(n) orΩ(n) dividesu
n
is of asymptotic density zero, where ω(n) and Ω(n) are the numbers of prime and prime power divisors ofn, respectively. The same also holds for the set of positive integersn such that τ(n)u
n
, where τ(n) is the number of the positive integer divisors of n, provided thatu
n
satisfies some mild technical conditions. 相似文献
6.
A. K. Varma 《Israel Journal of Mathematics》1972,12(4):337-341
Letx
kn=2θk/n,k=0,1 …n−1 (n odd positive integer). LetR
n(x) be the unique trigonometric polynomial of order 2n satisfying the interpolatory conditions:R
n(xkn)=f(xkn),R
n
(j)(xkn)=0,j=1,2,4,k=0,1…,n−1. We setw
2(t,f) as the second modulus of continuity off(x). Then we prove that |R
n(x)-f(x)|=0(nw2(1/nf)). We also examine the question of lower estimate of ‖R
n-f‖. This generalizes an earlier work of the author. 相似文献
7.
A. Hajnal 《Combinatorica》1985,5(2):137-139
We prove (in ZFC) that for every infinite cardinal ϰ there are two graphsG
0,G
1 with χ(G
0)=χ(G
1)=ϰ+ and χ(G
0×G
1)=ϰ. We also prove a result from the other direction. If χ(G
0)≧≧ℵ0 and χ(G
1)=k<ω, then χ(G
0×G
1)=k. 相似文献
8.
M. M. Gekhtman 《Mathematical Notes》1977,21(2):117-118
Let A>0 be an unbounded self-adjoint operator in a Hilbert space H. In the Hilbert space H1=L2 (0, π; H) we study the spectrum of the differential equations−y″(x)+Ay=λy, y (0)=y(π)=0,−y″(x)+Ay=λy, y′(0) =y′(π)=0. We find the principal terms of the asymptotics of the functions N(λ) for these problems and we ascertain the conditions
under which they are asymptotically not equivalent.
Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 209–212, February, 1977. 相似文献
9.
Bruno de Malafosse 《Acta Mathematica Hungarica》2004,104(3):241-263
We deal with the sum and the product of particular BK spaces and give necessary and sufficient conditions to have w
α(λ) + w
β(μ) = w
α
+β
(μ). Some results on matrix transformations mapping the space w
α(λ) + w
β(μ) into a given BK space are also given. This study generalizes some results obtained in [7] and [8].
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
10.
We consider the periodic boundary-value problem u
tt
− u
xx
= g(x, t), u(0, t) = u(π, t) = 0, u(x, t + ω) = u(x, t). By representing a solution of this problem in the form u(x, t) = u
0(x, t) + ũ(x, t), where u
0(x, t) is a solution of the corresponding homogeneous problem and ũ(x, t) is the exact solution of the inhomogeneous equation such that ũ(x, t + ω) u x = ũ(x, t), we obtain conditions for the solvability of the inhomogeneous periodic boundary-value problem for certain values of the
period ω. We show that the relation obtained for a solution includes known results established earlier.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 912–921, July, 2005. 相似文献
11.
We present necessary and sufficient conditions for uniform exponential expansiveness of discrete skew-product flows, in terms
of uniform complete admissibility of the pair (c
0(N, X), c
0(N, X)). We give discrete and continuous characterizations for uniform exponential expansiveness of linear skew-product flows,
using the uniform complete admissibility of the pairs (c
0(N, X), c
0(N, X)) and (C
0(R
+, X), C
0(R
+, X)), respectively. We generalize an expansiveness theorem due to Van Minh, R?biger and Schnaubelt, for the case of linear skew-product
flows.
Received August 10, 2001; in revised form June 25, 2002 相似文献
12.
We present necessary and sufficient conditions for uniform exponential expansiveness of discrete skew-product flows, in terms
of uniform complete admissibility of the pair (c
0(N, X), c
0(N, X)). We give discrete and continuous characterizations for uniform exponential expansiveness of linear skew-product flows,
using the uniform complete admissibility of the pairs (c
0(N, X), c
0(N, X)) and (C
0(R
+, X), C
0(R
+, X)), respectively. We generalize an expansiveness theorem due to Van Minh, R?biger and Schnaubelt, for the case of linear skew-product
flows. 相似文献
13.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
14.
LetX (Δ) be the real toric variety associated to a smooth fan Δ. The main purpose of this article is: (i) to determine the fundamental
group and the universal cover ofX (Δ), (ii) to give necessary and sufficient conditions on Δ under which π1(X(Δ)) is abelian, (iii) to give necessary and sufficient conditions on Δ under whichX(Δ) is aspherical, and when Δ is complete, (iv) to give necessary and sufficient conditions forC
Δ to be aK (π, 1) space whereC
Δ is the complement of a real subspace arrangement associated to Δ. 相似文献
15.
S. G. Khoma 《Ukrainian Mathematical Journal》2000,52(4):655-657
We find conditions for the existence of the classical solution of the boundary-value problem u
tt
-u
xx
= f(x,t), u(0,t)=u(π, t)=0, u(x, 0)=u(x, 2π). 相似文献
16.
We consider the problem of estimating the discriminant coefficients, η=∑1-(θ(1)-θ(2)) based on two independent normal samples fromN
p
(θ(1),∑) andN
p
(θ(2),∑). We are concerned with the estimation of η as the gradient of log-odds between two extreme situations. A decision theoretic
approach is taken with the quadratic loss function. We derive the unbiased estimator of the essential part of the risk which
is applicable for general estimators. We propose two types of new estimators and prove their dominance over the traditional
estimator using this unbiased estimator. 相似文献
17.
A. G. Baskakov 《Mathematical Notes》2000,67(6):690-698
We obtain conditions for the invertibility and the Fredholm property of the difference operator (Dx)(n)=x(n) -U(n)x(n − 1),n ε ℤ, in the Banach space l
p
(ℤ, X),p ε [1, ∞], of vector sequences, whereX is a Banach space andU is a bounded operator function.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 816–827, June, 2000. 相似文献
18.
Conditions for the existence and uniqueness of bounded solutions of nonlinear differential equations
V. Yu. Slyusarchuk 《Ukrainian Mathematical Journal》2009,61(2):320-335
We establish conditions required for the existence and uniqueness of bounded solutions of the nonlinear differential equation
f1( \fracdx(t)dt ) = f2( x(t) ) {f_1}\left( {\frac{{dx(t)}}{{dt}}} \right) = {f_2}\left( {x(t)} \right) , t ∈ ℝ. 相似文献
19.
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
20.
We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Ωε that is ε-periodically perforated by small holes of size O\mathcal {O}(ε). The holes are divided into two ε-periodical sets depending on the boundary interaction at their surfaces, and two different
nonlinear Robin boundary conditions σε(u
ε) + εκ
m
(u
ε) = εg
(m)
ε, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as ε → 0 and establish a convergence theorem without
using extension operators. An asymptotic approximation of the solution and the corresponding error estimate are also obtained.
Bibliography: 60 titles. Illustrations: 1 figure. 相似文献