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1.
Summary It is proved that if the nonempty intersection of bounded closed convex sets AnB is contained in (A + F)U(B+F) and one of the following holds true: (i) the space X is less-than-three dimensional, (ii) AUB is convex, (iii) F is a one-point set, then AnBCA+F or AnBCB+F (Theorems 2 and 3). Moreover, under some hypotheses the characterization of A and B such that AnB is a summand of AUB is given (Theorem 3).  相似文献   

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Summary In the paper we consider, from a topological point of view, the set of all continuous functionsf:I I for which the unique continuous solution:I – [0, ) of(f(x)) (x, (x)) and(x, (x)) (f(x)) (x, (x)), respectively, is the zero function. We obtain also some corollaries on the qualitative theory of the functional equation(f(x)) = g(x, (x)). No assumption on the iterative behaviour off is imposed.  相似文献   

5.
Arató  N.  Márkus  L. 《Analysis Mathematica》1986,12(4):307-312
Lu(t)+(u,F)g(t)=f(t), tS. , ( F, g). .

The authors wish to thank Professor Yu. A. Rozanov for his help and discussions.  相似文献   

6.
We consider solutions of the class of ODEs y=6y 2x , which contains the first Painlevé equation (PI) for =1. It is well known that PI has a unique real solution (called a tritronquée solution) asymptotic to and decaying monotonically on the positive real line. We prove the existence and uniqueness of a corresponding solution for each real nonnegative 1.  相似文献   

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An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G 0 where 0 andG 0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L 1-algebra, Fourier transforms of abelian groups are given and their properties are studied.  相似文献   

9.
The fundamental result of the paper is the following. Theorem: Let be a k-quasiconformal Jordan curve and let be another Jordan curve (not necessarily quasiconformal). Assume that f maps conformallyext ontoext , f()=, f()>0. We assume that there exists a homeomorphism between and such that Then there exist numbers =(k)>0 and A=A(k), such that f(())– A, .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 103–112, 1987.  相似文献   

10.
For each*-derivation of a separableC *-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x.  相似文献   

11.
We consider a functional differential equation (1) (t)=F(t,) fort[0,+) together with a generalized Nicoletti condition (2)H()=. The functionF: [0,+)×C 0[0,+)B is given (whereB denotes the Banach space) and the value ofF (t, ) may depend on the values of (t) fort[0,+);H: C 0[0,+)B is a given linear operator and B. Under suitable assumptions we show that when the solution :[0,+)B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2).  相似文献   

12.
N- (p, q) (1 pN-, L p - L q -. , , , L L q - , , .  相似文献   

13.
IfT is an isomorphism ofL (A, ) intoL (B, ) which satisfies the condition T T –11+, where (A, ) is a -finite measure space, thenT/T is close to an isometry with an error less than 4.  相似文献   

14.
A Single Server Poisson Input Queue with a Second Optional Channel   总被引:2,自引:0,他引:2  
Medhi  J. 《Queueing Systems》2002,42(3):239-242
Consider an M/G/1 queue such that over and above the first essential service having a general service time distribution, a unit may need a second optional service with another independent general service time. A unit may depart from the system either after the first essential service with probability (1–r) or at the end of the first service may immediately go for a second service with probability r (0r1). This is a generalization of a recent paper considered by Madan [5].  相似文献   

15.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

. . .  相似文献   

16.
Casazza  P.G.  Nielsen  N.J. 《Positivity》2001,5(4):297-321
In this paper we first show that if X is a Banach space and is a left invariant crossnorm on lX, then there is a Banach lattice L and an isometric embedding J of X into L, so that I J becomes an isometry of lX onto lm J(X). Here I denotes the identity operator on l and lm J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices.  相似文献   

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If X is a real Banach space, then the inequality x defines so-called hyperbolic cone in E=X. We develop a relevant version of Perron-Frobenius-Krein-Rutman theory.  相似文献   

19.
The polynomial, , is considered, where , r2 + . Let (f/d) be the Kronecker symbol and It is proved that Some number theoretic consequences of this result are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 183, pp. 155–164, 1990.  相似文献   

20.
A comprehensive class of cutting planes for the symmetric travelling salesman problem (TSP) is proposed which contains the known comb inequalities, the path inequalities and the 3-star constraints as special cases. Its relation to the clique tree inequalities is discussed. The cutting planes are shown to be valid for a relaxed version of the TSP, the travelling salesman problem on a road network, and—under certain conditions—to define facets of the polyhedron associated with this problem.  相似文献   

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