In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of - where is the open unit disc in and is the graph of a continuous valued function on - to higher dimensions, for certain classes of graphs 1$">. In particular, we show that Chirka's extension theorem generalizes to configurations in 1$">, involving graphs of (non-holomorphic) polynomial maps with small coefficients.
We define a quotient of bounded operators and on a Hilbert space with a kernel condition as the mapping , . A quotient is said to be positive symmetric if . In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient .
Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2X generated by F, let G be a Hausdorff commutative topological lattice group and let rbaF(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rbaF(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff. 相似文献
This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the -Lipschitz kernel of a given set-valued map as the largest -Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps. 相似文献
Extensions of crossed modules in Lie algebras with abelian kernel are studied, particularly backward and forward induced extensions and related properties. The set Opext((U, Q, ), (R, K, )) of congruence classes of extensions of (R, K, ) by (U, Q, ) is endowed with a K-vector space structure. This K-vector space appears in a five-term natural and exact sequence associated with an extension of crossed modules.2000 Mathematics Subject Classification: 17B56, 17B99, 18G99 相似文献
We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations. 相似文献
We introduce the notion of n-fold track extensions of a category C by a natural system D and prove that such extensions represent classes in the cohomology of C with coefficients in D introduced by Baues–Wirsching. This generalizes a result of Huebschmann on the cohomology of groups. 相似文献
This paper deals with n-monotone functionals, which constitute a generalisation of n-monotone set functions. Using the notion of exactness of a functional, we introduce a new notion of lower and upper integral which subsumes as particular cases most of the approaches to integration in the literature. As a consequence, we can characterise which types of integrals can be used to calculate the natural extension (the lower envelope of all linear extensions) of a positive bounded charge. 相似文献
Ample fields play an important role in possibility theory. These fields of subsets of a universe, which are additionally closed under arbitrary unions, act as the natural domains for possibility measures. A set provided with an ample field is then called an ample space. In this paper we generalise Wang's notions of product ample field and product ample space. We make a topological study of ample spaces and their products, and introduce ample subspaces, extensions and one-point extensions of ample spaces. In this way, a first step towards a mathematical theory of possibilistic processes is made. 相似文献