In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed...In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed the relation between them and recursive functions defined on other domains . It is indicated that the functions of natural numbers and/or symbol strings (words) are functions of CFLs. Several frequently used primitive recursive functions on words were given, including logical connectives, conditional expressions. Also the powerful operators (bounded maximization and minimization operators) for constructing primitive recursive functions were defined. Two important nontrivial algorithms, the characteristic function of arbitrary CFL and the parse function of CFL sentences were constructed. Based on them, the method for extending or restricting function domain was described.展开更多
Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known...Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.展开更多
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. I...Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. In this work we will be concerned with the relationship between bounded operators , and X-valued integrals on . When X is a Banach space, such relation has been completely achieved via Bochner integral in [1]. In this paper we investigate the context of locally convex spaces and we will focus attention on weak integrals, namely the Pettis integrals. Some results in this direction have been obtained, under some special conditions on the structure of X and its topological dual X*. In this work we consider the case of a semi reflexive locally convex space and prove that each Pettis integral with respect to a signed measure μ, on S gives rise to a unique bounded operator , which has the given Pettis integral form.展开更多
In the present article, certain classes of generalized p-valent Robertson functions are considered. Mapping properties of these classes are investigated under certain p-valent integral operators introduced by Frasin r...In the present article, certain classes of generalized p-valent Robertson functions are considered. Mapping properties of these classes are investigated under certain p-valent integral operators introduced by Frasin recently.展开更多
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operat...In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.展开更多
For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in additi...For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .展开更多
It was conjectured by the first author and Peetre that the higher Laplace-Beltrami opera- tors generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains...It was conjectured by the first author and Peetre that the higher Laplace-Beltrami opera- tors generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains of rank 〈 6 by using a graph manipulation of Kahler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain.展开更多
In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈（（lp）T,l∞）, where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient co...The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈（（lp）T,l∞）, where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient conditions were established in almost all of those cases, by using the Hausdorff measure of noncompactness. We improve those results by applying another method for the characterizations of compact linear operators between BK spaces.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69873042) .
文摘In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed the relation between them and recursive functions defined on other domains . It is indicated that the functions of natural numbers and/or symbol strings (words) are functions of CFLs. Several frequently used primitive recursive functions on words were given, including logical connectives, conditional expressions. Also the powerful operators (bounded maximization and minimization operators) for constructing primitive recursive functions were defined. Two important nontrivial algorithms, the characteristic function of arbitrary CFL and the parse function of CFL sentences were constructed. Based on them, the method for extending or restricting function domain was described.
基金supported by the National Natural Science Foundation of China(Grant No.11971403)the Natural Science Foundation of Fujian Province of China(Grant No.2019J01024)。
文摘Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘 Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
文摘Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. In this work we will be concerned with the relationship between bounded operators , and X-valued integrals on . When X is a Banach space, such relation has been completely achieved via Bochner integral in [1]. In this paper we investigate the context of locally convex spaces and we will focus attention on weak integrals, namely the Pettis integrals. Some results in this direction have been obtained, under some special conditions on the structure of X and its topological dual X*. In this work we consider the case of a semi reflexive locally convex space and prove that each Pettis integral with respect to a signed measure μ, on S gives rise to a unique bounded operator , which has the given Pettis integral form.
文摘In the present article, certain classes of generalized p-valent Robertson functions are considered. Mapping properties of these classes are investigated under certain p-valent integral operators introduced by Frasin recently.
文摘In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.
文摘For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
基金supported by GA CR(Grant No.201/12/G028)RVO funding for IC(Grant No.67985840)
文摘It was conjectured by the first author and Peetre that the higher Laplace-Beltrami opera- tors generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains of rank 〈 6 by using a graph manipulation of Kahler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain.
基金Department of Mathematics and Statistics,Auburn University,AL,USA
文摘In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
文摘The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈（（lp）T,l∞）, where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient conditions were established in almost all of those cases, by using the Hausdorff measure of noncompactness. We improve those results by applying another method for the characterizations of compact linear operators between BK spaces.
