共查询到20条相似文献,搜索用时 632 毫秒
1.
Let X, Y be Banach spaces and M be a linear subspace in X × Y = {{x, y}|x ∈ X, y ∈ Y }. We may view M as a multi-valued linear operator from X to Y by taking M (x) = {y|{x, y} ∈ M }. In this paper, we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M . The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces. 相似文献
2.
Helena Malinowski 《Positivity》2018,22(4):1039-1063
In Archimedean vector lattices bands can be introduced via three different coinciding notions. First, they are order closed ideals. Second, they are precisely those ideals which equal their double disjoint complements. The third concept is that of an ideal which contains the supremum of any of its bounded subsets, provided the supremum exists in the vector lattice. We investigate these three notions and their relationships in the more general setting of Archimedean pre-Riesz spaces. We introduce the notion of a supremum closed ideal, which is related to the third aforementioned notion in vector lattices. We show that for a directed ideal I in a pervasive pre-Riesz space with the Riesz decomposition property these three concepts coincide, provided the double disjoint complement of I is directed. In pervasive pre-Riesz spaces every directed band is supremum closed and every supremum closed directed ideal I equals its double disjoint complement, provided the double disjoint complement of I is directed. In general, in Archimedean pre-Riesz spaces the three notions differ. For this we provide appropriate counterexamples. 相似文献
3.
研究了保不交算子值域的性质,建立了保不交算子值域为Riesz子空间的一个刻画;又讨论了主理想和主带在保不交算子作用后的象的性质,一些相关结果也得以讨论. 相似文献
4.
We consider a family of Newton-type iterative processes solving nonlinear equations in Banach spaces, that generalizes the
usually iterative methods of R-order at least three. The convergence of this family in Banach spaces is usually studied when the second derivative of the
operator involved is Lipschitz continuous and bounded. In this paper, we relax the first condition, assuming that ‖F″(x)−F″(y)‖≤ω(‖x−y‖), where ω is a nondecreasing continuous real function. We prove that the different R-orders of convergence that we can obtain depend on the quasihomogeneity of the function ω. We end the paper by applying the study to some nonlinear integral equations.
This work was supported by the Ministry of Science and Technology (BFM 2002-00222), the University of La Rioja (API-04/13)
and the Government of La Rioja (ACPI 2003/2004). 相似文献
5.
Mohamed Ali Toumi 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):499-508
The main purpose of this paper is the following Theorem: letE be a Dedekind complete Riesz space (vector lattice), letA be a vector subspace of it which majorizesE and letx
0 be an element ofE−A. IfT
0 is a positive projection onA, then there existsy
0∈E such thatT
0 can be extended to a positive projection onA+ℝx
0+ℝy
0. 相似文献
6.
A directed triple system of order v with index λ, briefly by DTS(v,λ), is a pair (X, B) where X is a v-set and B is a collection of transitive triples (blocks) on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS(v, λ) is a DTS(v, λ) without repeated blocks. A simple DTS(v, ),) is called pure and denoted by PDTS(v, λ) if (x, y, z) ∈ B implies (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y) B. A large set of disjoint PDTS(v, λ), denoted by LPDTS(v, λ), is a collection of 3(v - 2)/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS(v, λ) are presented. Especially, we determine the spectrum of LPDTS(v, 2). 相似文献
7.
E. Preissmann 《Aequationes Mathematicae》1987,32(1):195-212
We solve independently the equations 1/θ(x)θ(y)=ψ(x)−ψ(y)+φ(x−y)/θ(x−y) and 1/θ(x)θ(y)=σ(x)−σ(y)/θ(x−y)+τ(x)τ(y), τ(0)=0. In both cases we find θ2=aθ4+bθ2+c. We deduce estimates for the spectral radius of a matrix of type(1/θ(x
r
−x
s
)) (the accent meaning that the coefficients of the main diagonal are zero) and we study the case where thex
r
are equidistant.
Dédié to à Monsieur le Professeur Otto Haupt à l'occasion de son cententiare avec les meilleurs voeux 相似文献
8.
Ignacy Kotlarski 《Annali di Matematica Pura ed Applicata》1966,74(1):129-134
Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x1, x2, …, xn be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals fk(t) = E[ei(t,x
k)], (k=1, 2, …, n): let y1=x1 + xn, y2=x2 + xn, …, yn−1=xn−1 + xn.
If the characteristic functional f(t1, t2, …, tn−1) of the random variables (y1, y2, …, yn−1) does not vanish, then the joint distribution of (y1, y2, …, yn−1) determines all the distributions of x1, x2, …, xn up to change of location. 相似文献
9.
Restricted Fault Diameter of Hypercube Networks 总被引:1,自引:0,他引:1
This paper studies restricted fault diameter of the n-dimensional hypercube networks Qn (n ≥ 2).It is shown that for arbitrary two vertices x and y with the distance d in Qn and any set F with at most 2n-3 vertices in Qn - {x, y}, if F contains neither of neighbor-sets of x and y in Qn, then the distance between x andy in Qn - F is given by D(Qn-F;x,y){=1 , for=1;≤d 4 , for 2≤d≤n-2,n≥4;≤n 1, for d=n-1,n≥3; =n, for d=n. Furthermore, the upper bounds are tight. As an immediately consequence, Qn can tolerate up to 2n-3 vertices failures and remain diameter 4 if n = 3 and n 2 if n ≥ 4 provided that for each vertex x in Qn, all the neighbors of x do not fail at the same time. This improves Esfahanian‘s result. 相似文献
10.
N. A. Kachanovskii 《Ukrainian Mathematical Journal》1999,51(10):1503-1511
Pseudodifferential equations of the formv(Dx)y=f (here,v is a function holomorphic at zero andD
x is a pseudodifferential operator) are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis.
The results obtained are applied to the construction of a generalized translation operatorT
y
χ
=χ(<y, Dχ>) on the spaces indicated and to the investigation of its properties. In particular, we prove the associativity, commutativity,
and other properties ofT
y
χ
, which are analogs of the classical properties of a generalized translation operator.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51,
No. 10, pp. 1334–1341, October, 1999. 相似文献
11.
In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator
whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation
does not exceed the sum of properly chosen least upper bounds in m-and ((N − m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 12–19, January, 2006. 相似文献
12.
A real multivariate polynomial p(x
1, …, x
n
) is said to sign-represent a Boolean function f: {0,1}
n
→{−1,1} if the sign of p(x) equals f(x) for all inputs x∈{0,1}
n
. We give new upper and lower bounds on the degree of polynomials which sign-represent Boolean functions. Our upper bounds
for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds
since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs. 相似文献
13.
A set U of vertices of a graph G is called a geodetic set if the union of all the geodesics joining pairs of points of U is the whole graph G. One result in this paper is a tight lower bound on the minimum number of vertices in a geodetic set. In order to obtain
that result, the following extremal set problem is solved. Find the minimum cardinality of a collection 𝒮 of subsets of [n]={1,2,…,n} such that, for any two distinct elements x,y∈[n], there exists disjoint subsets A
x
,A
y
∈𝒮 such that x∈A
x
and y∈A
y
. This separating set problem can be generalized, and some bounds can be obtained from known results on families of hash functions.
Received: May 19, 2000 Final version received: July 5, 2001 相似文献
14.
An increasing sequence of realsx=〈x
i
:i<ω〉 is simple if all “gaps”x
i
+1−x
i
are different. Two simple sequencesx andy are distance similar ifx
i
+1−x
i
<x
j
+1−x
j
if and only ify
i
+1−y
i
<y
j
+1−y
j
for alli andj. Given any bounded simple sequencex and any coloring of the pairs of rational numbers by a finite number of colors, we prove that there is a sequencey distance similar tox all of whose pairs are of the same color. We also consider many related problems and generalizations.
Partially supported by OTKA-4269.
Partially supported by NSF grant STC-91-19999.
Partially supported by OTKA-T-020914, NSF grant CCR-9424398 and PSC-CUNY Research Award 663472. 相似文献
15.
Let T be an order bounded disjointness preserving operator on an Archimedean vector lattice. The main result in this paper shows
that T is algebraic if and only if there exist natural numbers m and n such that n ≥ m, and Tn!, when restricted to the vector sublattice generated by the range of Tm, is an algebraic orthomorphism. Moreover, n (respectively, m) can be chosen as the degree (respectively, the multiplicity of 0 as a root) of the minimal polynomial of T. In the process of proving this result, we define strongly diagonal operators and study algebraic order bounded disjointness
preserving operators and locally algebraic orthomorphisms. In addition, we introduce a type of completeness on Archimedean
vector lattices that is necessary and sufficient for locally algebraic orthomorphisms to coincide with algebraic orthomorphisms. 相似文献
16.
It is known that if a rearrangement invariant function space E on [0,1] has an unconditional basis then each linear continuous operator on E is a sum of two narrow operators. On the other hand, the sum of two narrow operators in L1 is narrow. To find a general approach to these results, we extend the notion of a narrow operator to the case when the domain
space is a vector lattice. Our main result asserts that the set Nr(E, F) of all narrow regular operators is a band in the vector lattice Lr(E, F) of all regular operators from a non-atomic order continuous Banach lattice E to an order continuous Banach lattice F. The band generated by the disjointness preserving operators is the orthogonal complement to Nr(E, F) in Lr(E, F). As a consequence we obtain the following generalization of the Kalton-Rosenthal theorem: every regular operator T : E → F from a non-atomic Banach lattice E to an order continuous Banach lattice F has a unique representation as T = TD + TN where TD is a sum of an order absolutely summable family of disjointness preserving operators and TN is narrow.
Supported by Ukr. Derzh. Tema N 0103Y001103. 相似文献
17.
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
18.
Summary Based on a random sample from the normal cumulative distribution function ϕ(x; μ, σ) with unknown parameters μ and σ, one-sided confidence contours for ϕ(x; μ, σ), −∞<x<∞, and simultaneous confidence intervals for ϕ(y; μ, σ)−ϕ(x; μ, σ), −∞<x<y<∞, are constructed using the method outlined in [3]. Small sample and asymptotic distributions of the relevant statistics
are provided so that the construction could be completely carried out in any practical situation. 相似文献
19.
In a recent paper, Pawale (Des Codes Cryptogr, 2010) investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x + 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D{\mathcal{D}} is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper,
quasi-symmetric designs with y − x = 3 are investigated. It is shown that such a design or its complement has parameter set which is one of finitely many which
are listed explicitly or λ ≤ x + 4 or 0 ≤ x ≤ 1 or the pair (λ, x) is one of (7, 2), (8, 2), (9, 2), (10, 2), (8, 3), (9, 3), (9, 4) and (10, 5). It is also shown that there are no triangle-free
quasi-symmetric designs with positive intersection numbers x and y with y = x + 3. 相似文献
20.
Igor Kukavica 《Journal d'Analyse Mathématique》1995,67(1):269-280
We establish sharp upper bounds on the (n−1)-dimensional Hausdorff measure of the zero (nodal) sets and on the maximal order of vanishing corresponding to eigenfunctions
of a regular elliptic problem on a bounded domain Ω ⊆ ℝ
n
with real-analytic boundary. The elliptic operator may be of an arbitrary even order, and its coefficients are assumed to
be real-analytic. This extends a result of Donnelly and Fefferman ([DF1], [DF3]) concerning upper bounds for nodal volumes
of eigenfunctions corresponding to the Laplacian on compact Riemannian manifolds with boundary. 相似文献