共查询到20条相似文献,搜索用时 31 毫秒
1.
Larbi Alaoui 《Semigroup Forum》2001,63(3):330-356
In this paper nonlinear homogeneous retarded differential equations and models from population dynamics and epidemiology
are considered and studied by the use of translation semigroup theory. We show that the corresponding solution semigroups
are equivalent to appropriate translation semigroups. Existence results for the retarded equations are established by taking
the space of initial functions of the form W
1,p
((-r,0),F) where F is a Banach space, 1≤ p<∈fty and 0<r\le∈fty .
June 28, 1999 相似文献
2.
Jiguang Bao 《中国科学A辑(英文版)》1998,41(10):1047-1050
Under the mild conditions, it is proved that the convex surface is global C1.1, with the given Gaussian curvature 0≤K ∈ C
0
∞
and the given boundary curve. Examples are given to show that the regularity is optimal.
Project supported by the Doctoral Funds of China and the National Natural Science Foundation of China (Grant No. 19771009). 相似文献
3.
We consider the best approximation of some function classes by the manifold M
n
consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W
p
r,d
from the manifold M
n
in the space L
q
for any 2≤ q≤ p≤∈fty behaves asymptotically as n
-r/(d-1)
. In particular, we obtain this asymptotic estimate for the uniform norm p=q=∈fty .
January 10, 2000. Date revised: March 1, 2001. Date accepted: March 12, 2001. 相似文献
4.
Existence of the mild solution for some fractional differential equations with nonlocal conditions 总被引:1,自引:0,他引:1
We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential
equation with nonlocal conditions: D
q
x(t)=Ax(t)+t
n
f(t,x(t),Bx(t)), t∈[0,T], n∈ℤ+, x(0)+g(x)=x
0, where 0<q<1, A is the infinitesimal generator of a C
0-semigroup of bounded linear operators on a Banach space X. 相似文献
5.
Peculiar properties of hermitian and positive n-times integrated C-cosine functions on Banach spaces are investigated. Among them are: (1) Any nondegenerate positiven -times integrated C-cosine function is infinitely differentiable in operator norm; (2) An exponentially bounded, nondegenerateC -cosine function on L
p
() (1
L 1(), C0 , in case C has dense range) is positive if and only if its generator is bounded, positive, and commutes with C. 相似文献
6.
L. Baratchart V. A. Prokhorov E. B. Saff 《Foundations of Computational Mathematics》2001,1(4):385-416
Let E \subset(-1,1) be a compact set, let μ be a positive Borel measure with support \supp μ =E , and let H
p
(G),
1≤ p ≤∈fty, be the Hardy space of analytic functions on the open unit disk G with circumference Γ={z \colon |z|=1} . Let Δ
n,p
be the error in best approximation of the Markov function \frac{1}{2π i} ∈t_E \frac{d μ(x)}{z-x} in the space L
p
(Γ) by meromorphic functions that can be represented in the form h=P/Q , where P ∈ H
p
(G),
Q is a polynomial of degree at most n , Q\not \equiv 0 . We investigate the rate of decrease of Δ
n,p
,
1≤ p ≤∈fty , and its connection with n -widths. The convergence of the best meromorphic approximants and the limiting distribution of poles of the best approximants
are described in the case when 1<p≤∈fty and the measure μ with support E=[a,b] satisfies the Szegő condition ∈t_a^b \frac{\log(d μ/ d x)}{\sqrt{(x-a)(b-x)}} dx >- ∈fty.
July 27, 2000. Final version received: May 19, 2001. 相似文献
7.
Shang Quan Bu 《数学学报(英文版)》2012,28(1):37-44
We study the well-posedness of the equations with fractional derivative Dαu(t)=Au(t)+f(t)(0 ≤t≤2π),where A is a closed operator in a Banach space X,0α1 and Dα is the fractional derivative in the sense of Weyl.Although this problem is not always well-posed in Lp(0,2π;X) or periodic continuous function spaces Cper([0,2π];X),we show by using the method of sum that it is well-posed in some subspaces of L p(0,2π;X) or C per([0,2π];X). 相似文献
8.
F. A. Sukochev 《Israel Journal of Mathematics》2000,115(1):137-156
We classify, up to a linear-topological isomorphism, all separableL
p-spaces, 1≤p<∞, associated with von Neumann algebras of type I. In particular, anyL
p-space associated with an infinite-dimensional atomic von Neumann algebra is isomorphic tol
p, or toC
p, or to
. Further, anyL
p-space,p∈[1,∞),p∈2 associated with an infinite-dimensional von Neumann algebraM of type I is isomorphic to one of the following nine Banach spaces: lp, Lp, SP, Cp, Sp ⊕ Lp, Lp(Sp), Cp ⊕ Lp, Lp(Cp), Cp ⊕ Lp(Sp). In the casep=1 all the spaces in this list are pairwise non-isomorphic.
Research supported by the Australian Research Council. 相似文献
9.
Horst R. Thieme 《Journal of Evolution Equations》2008,8(2):283-305
If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L
1(0, b, X), the convolution of T with f is defined by . It is shown that T * f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T * f is continuously differentiable for all f ∈ L
p
(0, b, X) (1 ≤ p < ∞) if and only if T is of bounded semi-p-variation on [0, b] and T(0) = 0. If T is an integrated semigroup with generator A, these respective conditions are necessary and sufficient for the Cauchy problem u′ = Au + f, u(0) = 0, to have integral (or mild) solutions for all f in the respective function vector spaces. A converse is proved to a well-known result by Da Prato and Sinestrari: the generator
A of an integrated semigroup is a Hille-Yosida operator if, for some b > 0, the Cauchy problem has integral solutions for all f ∈ L
1(0, b, X). Integrated semigroups of bounded semi-p-variation are preserved under bounded additive perturbations of their generators and under commutative sums of generators
if one of them generates a C
0-semigroup.
Günter Lumer in memoriam 相似文献
10.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
11.
V. N. Konovalov 《Ukrainian Mathematical Journal》2005,57(12):1911-1936
Let s ∈ ℕ and let Δ
+
s
be the set of functions x: I ↦ ℝ on a finite interval I such that the divided differences [x; t
0, ..., t
s
] of order s of these functions are nonnegative for all collections of s + 1 different points t
0, ..., t
s
∈ I. For the classes Δ
+
s
B
p
: = Δ
+
s
∩ B
p
, where B
p
is the unit ball in L
p
, we determine the orders of Kolmogorov and linear widths in the spaces Lq
for 1 ≤ q > p ≤ ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1633–1652, December, 2005. 相似文献
12.
Q. X. Yang 《Proceedings Mathematical Sciences》2005,115(3):347-368
In this paper, we characterize the symbol in Hormander symbol classS
ρ
m
,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classS
ρ
m
,δ (m ∈R, ρ > 0, δ≥ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishL
p
(1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets,
and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients
in phase space. 相似文献
13.
Pei-Kee Lin 《Semigroup Forum》1996,53(1):208-211
For any complex Banach spaceX, letJ denote the duality mapping ofX. For any unit vectorx inX and any (C
0) contraction semigroup (T
t
)
t>0 onX, Baillon and Guerre-Delabriere proved that ifX is a smooth reflexive Banach space and if there isx
*∈J(x) such that ÷〈(T(t)x, J(x)〈÷→1 ast→∞, then there is a unit vectory∈X which is an eigenvector of the generatorA of (T
t
)
t>0 associated with a purely imaginary eigenvalue. They asked whether this result is still true ifX is replaced byc
0. In this article, we show the answer is negative
Partial results of this paper were obtained when the author attended the International Conference of Convexity at the University
of Marne-La-Vallée. He would like to express his gratitude for the kind hospitality offered to him. He would also like to
thank Profs. Goldstein and Jamison for their valuable suggestions. 相似文献
14.
Sandra Cerrai 《Probability Theory and Related Fields》1999,113(1):85-114
In the present paper we consider the transition semigroup P
t
related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in
the Banach space of continuous functions , where ⊂ℝ
d
is a bounded open set. In L
2() the only result proved is the strong Feller property, for d=1. Here we are able to prove that if f∈C
∞(ℝ) and d≤3, then for any and t>0. An important application is to the study of the ergodic properties of the system. These results are also of interest for
some problem in stochastic control.
Received: 20 August 1997 / Revised version: 27 May 1998 相似文献
15.
In this paper, a natural R
+
n+1
extension of singular integrals, i.e.,T
κ:f→K*φ
t
*t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C1 and u-Mw, w∈A∞, then Tk is of type (Lp(udx), Lp(dμ)). As a related topic, a maximal operator
is proved to be of type
, where
, provided (dμ, udx) ∈C1 and u∈ A∞.
Supported by National Science Foundation of China 相似文献
16.
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
17.
The purpose of this paper is to study the L
2 boundedness of operators of the form f ↦ ψ(x) ∫ f (γ
t
(x))K(t)dt, where γ
t
(x) is a C
∞ function defined on a neighborhood of the origin in (t, x) ∈ ℝ
N
× ℝ
n
, satisfying γ
0(x) ≡ x, ψ is a C
∞ cut-off function supported on a small neighborhood of 0 ∈ ℝ
n
, and K is a “multi-parameter singular kernel” supported on a small neighborhood of 0 ∈ ℝ
N
. The goal is, given an appropriate class of kernels K, to give conditions on γ such that every operator of the above form is bounded on L
2. The case when K is a Calderón-Zygmund kernel was studied by Christ, Nagel, Stein, and Wainger; we generalize their conditions to the case
when K has a “multi-parameter” structure. For example, when K is given by a “product kernel.” Even when K is a Calderón- Zygmund kernel, our methods yield some new results. This is the first paper in a three part series, the later
two of which are joint with E. M. Stein. The second paper deals with the related question of L
p
boundedness, while the third paper deals with the special case when γ is real analytic. 相似文献
18.
We study the injectivity properties of the spherical mean value operators associated to the Gelfand pairs (H
n,K), whereK is a compact subgroup ofU(n). We show that these spherical mean value operators are injective onL
p Hn) for 1≤p<∞. Forp=∞, these operators are not injective. Nevertheless, if the spherical meansf*μ
i
overK-orbits of sufficiently many points (z
i,t
i) ∈H
n vanish, we identify a necessary and sufficient condition on the points (z
i,t
i) which guaranteesf=0. ForK=U(n), this is equivalent to the condition for the two-radius theorem.
Research supported by N.B.H.M. Research Grant, Govt. of India. 相似文献
19.
B. Beckermann 《Constructive Approximation》2000,16(3):427-448
It is shown that a conjecture of E. A. Rakhmanov is true concerning the zero distribution of orthogonal polynomials with
respect to a measure having a discrete real support. We also discuss the case of extremal polynomials with respect to some
discrete L
p
-norm, 0 < p ≤∈fty , and give an extension to complex supports.
Furthermore, we present properties of weighted Fekete points with respect to discrete complex sets, such as the weighted
discrete transfinite diameter and a weighted discrete Bernstein—Walsh-like inequality.
August 24, 1998. Date revised: March 26, 1999. Date accepted: April 27, 1999. 相似文献
20.
LetT(t) be the translation group onY=C
0(ℝ×K)=C
0(ℝ)⊗C(K),K compact Hausdorff, defined byT(t)f(x, y)=f(x+t, y). In this paper we give several representations of the sun-dialY
⊙ corresponding to this group. Motivated by the solution of this problem, viz.Y
⊙=L
1(ℝ)⊗M(K), we develop a duality theorem for semigroups of the formT
0(t)⊗id on tensor productsZ⊗X of Banach spaces, whereT
0(t) is a semigroup onZ. Under appropriate compactness assumptions, depending on the kind of tensor product taken, we show that the sun-dial ofZ⊗X is given byZ
⊙⊗X*. These results are applied to determine the sun-dials for semigroups induced on spaces of vector-valued functions, e.g.C
0(Ω;X) andL
p
(μ;X).
This paper was written during a half-year stay at the Centre for Mathematics and Computer Science CWI in Amsterdam. I am grateful
to the CWI and the Dutch National Science Foundation NWO for financial support. 相似文献