共查询到20条相似文献,搜索用时 24 毫秒
1.
Jean Saint Raymond 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):162-168
Let (T, ℐ, μ) be a σ-finite atomless measure space,p∈[1,∞),E a real Banach space andf a measurable function:E xT→ℝ. We denote byF the functionalF:
and byDom(F) its domain, it is the set {uεL
p(T,E):ū(t)=f(u),t)εL
1(T)}, and we prove that the sublevelsS(λ)={u:F(u)≤λ} are all connected in the subspaceDom(F) of the Banach spaceL
p(T, E). 相似文献
2.
It is proved that for every reflexive Orlicz spaceX there is a functionn(k,ε) so that wheneverE is ak-dimensional subspace ofX there exists an operatorT: X→X such thatT
1E=identity, ‖T‖≦1+ε and dimTX≦n(k,ε). Some general facts concerning the uniform approximation property are also presented.
Research of the first named author was partially supported by NSF Grant MPS 74-07509-A01. 相似文献
3.
I. I. Antypko 《Ukrainian Mathematical Journal》1998,50(5):822-830
We consider a solution u(x, t) of the general linear evolution equation of the second order with respect to time variable given on the ball Π(T) = {(x,t): xε R
n, t ε [0, T]} and study the dependence of the behavior of this solution on the behavior of the functions at infinity.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 724–731, May, 1998. 相似文献
4.
Eugene Wesley 《Israel Journal of Mathematics》1973,14(1):104-114
Using the method of forcing of set theory, we prove the following two theorems on the existence of measurable choice functions:
LetT be the closed unit interval [0,1] and letm be the usual Lebesgue measure defined on the Borel subsets ofT. Theorem1. LetS⊂T×T be a Borel set such that for alltεT,S
t
def={x|(t,x)εS} is countable and non-empty. Then there exists a countable series of Lebesgue-measurable functionsf
n: T→T such thatS
t={fn(t)|nεω} for alltε[0,1],W
x={y|(x,y)εW} is uncountable. Then there exists a functionh:[0,1]×[0,1]→W with the following properties: (a) for each xε[0,1], the functionh(x,·) is one-one and ontoW
x and is Borel measurable; (b) for eachy, h(·, y) is Lebesgue measurable; (c) the functionh is Lebesgue measurable. 相似文献
5.
Israel Aharoni 《Israel Journal of Mathematics》1974,19(3):284-291
It is shown that there is a constantK so that, for every separable metric spaceX, there is a mapT:X →c
o satisfyingd(x, y)≦‖Tx−Ty‖≦Kd(x, y) for everyx, y ∈ X.
This is a part of the author's Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Professor
J. Lindenstrauss. 相似文献
6.
YANGZUODONG 《高校应用数学学报(英文版)》1997,12(4):399-410
In this paper,the nonexistence of positive entire solutions for div(|Du|^1-2Du)≥q(x)f(u),x∈R^N,is establisbed,where p>1,DU=(D,u……dnu),qsR^N→(o,∞)and f2(0,∞)→(o,∞)are continuous functions. 相似文献
7.
We consider the family {X
, 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is
t
X
=
X
+b({X
})+({X
})
. Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X
}A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes. 相似文献
8.
Eduardo H. Zarantonello 《Israel Journal of Mathematics》1973,15(2):158-166
It is shown that the set of points for which a monotone mappingT:X→X
* from a separable Banach space into its dual is not single-valued has no interior; if dimX<∞ and intD(T)≠ϕ then the set has Lebesgue measure zero. Moreover, for accretive mappingsT:X→X from a separable Banach space into itself, the dimension of the set of points whose images contain balls of codimension not
larger thank does not exceedk. Applications to convexity are given. 相似文献
9.
Nicolae H. Pavel 《Israel Journal of Mathematics》1983,46(1-2):103-122
LetX be a real Banach space and letA∶D(A)⊂X→X be the (linear) infinitesimal generator of the semigroupS(t) of classC
0 (of type ω). Assume that the function (t,x)→F(t,x) is continuous, the domainD(t)=D(F(t,·)) is such thatt→D(t) is closed and for eacht∈(a,b), the operatorx→F(t,x) is dissipative. One proves that the subtangential condition (A5) is necessary and sufficient for the existence of the mild
solution to the equationu′=Au+F(t,u). All previous results of this type are included here. An elementary method for proving the uniqueness is pointed out and
applications to PDE are given. 相似文献
10.
Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(X
ε (t)): ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψ_ε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X ε (t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ_ε(u) and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient
law for the simulation of Ψ_ε(u).
AMS Subject Classifications 60F10, 91B30
This work has been partially supported by Murst Project “Metodi Stocastici in Finanza Matematica” 相似文献
11.
Rainer Wittmann 《Israel Journal of Mathematics》1987,59(1):8-28
LetT be a positive linear contraction inL
p (1≦p<∞), then we show that lim ‖T
pf −T
n+1
f‖
p
≦(1 − ε)21/p
(f∈L
p
+
, ε>0 independent off) implies already limn
n→∞ ‖T
nf −T
n+1
n+1f ‖p
p=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown. 相似文献
12.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
13.
Alexander Šostak 《Journal of Mathematical Sciences》2007,144(5):4527-4534
Given an M-valued equality E: X×X → M on a set X, we extend it to the M-valued equality ε: L
X
× L
X
→ M on the L-powerset L
X
of X, where L is a complete sublattice of a GL-monoid M. As a result, we come to a category SET(M,L) whose objects are quadruples (X,E,L
X
, ε). This category serves as a ground category for the category L-TOP(M) of (L,M)-valued topological spaces and some of its subcategories, which are the main subject of this paper. In particular, as special
cases, we obtain here Chang-Goguen, Lowen, Kubiak-Šostak, and some other known categories related to fuzzy topology.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 237–247, 2005. 相似文献
14.
Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type 总被引:17,自引:0,他引:17
W. A. Kirk 《Israel Journal of Mathematics》1974,17(4):339-346
LetX be a Banach space,K a nonempty, bounded, closed and convex subset ofX, and supposeT:K→K satisfies: for eachx∈K, lim sup
i→∞{sup
y∈K
‖t
ix−Tiy∼−‖x−y‖}≦0. IfT
N is continuous for some positive integerN, and if either (a)X is uniformly convex, or (b)K is compact, thenT has a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→K satisfying, fori sufficiently large, ‖Tix−Tiy‖≦k
i‖x−y∼,x,y∈K, wherek
i→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of
convexity, ɛ0 (X), be less than one.
Research supported by National Science Foundation Grant GP 18045. 相似文献
15.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
16.
Nonexistence of invariant graphs in all supercritical energy levels of mechanical Lagrangians in T
2
Rafael O. Ruggiero 《Bulletin of the Brazilian Mathematical Society》2006,37(3):419-449
Let (T2, g) be a smooth Riemannian structure in the torus T2. We show that given ε > 0 and any C∞ function U : T2 → ℝ there exists a C1 function Uε with Lipschitz derivatives that is ε-C0 close to U for which there are no continuous invariant graphs in any supercritical energy level of the mechanical Lagrangian Lε : TT2 → ℝ given by
. We also show that given n ∈ ℕ, the set of C∞ potentials U : T2 → ℝ for which there are no continuous invariant graphs in any supercritical energy level E ≤ n of
is C0 dense in the set of C∞ functions.
Partially supported by CNPq, FAPERJ-Cientistas do nosso estado. 相似文献
17.
Dieter Bothe 《Israel Journal of Mathematics》1998,108(1):109-138
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,a]×X→2
X
, we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x
0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))≤k(t)β(B) for all boundedB⊂X wherek∈L
1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR
δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC
o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists.
The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE. 相似文献
18.
Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id
X
)=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id
X
) contains all non-invertible transformations in C(id
X
). 相似文献
19.
It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. 相似文献
20.
Vladimir Semenovich Korolyuk 《Journal of Mathematical Sciences》2011,179(2):273-289
Three main schemes of limit theorems for random evolutions are discussed: averaging, diffusion approximation, and the asymptotics
of large deviations. Markov stochastic evolutions with locally independent increments on increasing time intervals T
ε
= t/ε → ∞, ε → 0, are considered. The asymptotic behavior of random evolutions is investigated with the use of solutions of the singular perturbation
problems for reducibly invertible operators. 相似文献