* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology Harbin 150001, P.R.China Full list of author information is available at the end of the article Abstract We establish the Poincaré-type inequalities for the composition of the LaplaceBeltrami operator and the Green’s operator applied to the solutions of the nonhomogeneous A-harmonic equation in the Joh...

We discuss compactness of the ∂-Neumann operator in the setting of weighted Lspaces on Cn. For this purpose we use a description of relatively compact subsets of Lspaces. We also point out how to use this method to show that property (P) implies compactness for the ∂-Neumann operator on a smoothly bounded pseudoconvex domain and mention an abstract functional analysis characterization of compac...

The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general Lp-spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banac...

Abstract In this paper we consider the lower order eigenvalues of biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a type of general inequalities for them. In particular, we study the lower order eigenvalues of biharmonic operator on compact submanifolds of Euclidean spaces, of spheres, and of projective spaces. We obtain some estimates for lower orde...

Abstract. In this paper we obtain a necessary and sufficient condition for the canonical solution operator to ∂ restricted to radial symmetric Bergman spaces to be a Hilbert-Schmidt operator. We also discuss compactness of the solution operator in spaces of entire functions in one variable. In the sequel we consider several examples and also treat the case of weighted spaces of entire functions...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...

Abstract. We study a general transition operator, generated by a random walk on a graph X ; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from l(X) into itself. Moreover we characterize compact operators and we relate this property to the behaviour of the associated random walk. We give a necessary ...

We give some new characterizations, of unitaries, isometries, unital operator spaces, unital function spaces, operator systems, C-algebras, and related objects. Several characterizations of these objects are already known; see e.g. [15, Theorem 9.5.16], [1], the discussion on p. 316 of [4], [14], and [13]. One difference between our paper and these cited references, is that our results only use...

Multiway Decision Graphs (MDGs) are a canonical representation of a subset of many-sorted first-order logic. It generalizes classical BDDs with abstract data and uninterpreted functions. In this paper, we describe a new MDG construction based on the GeneralizedIf-Then-Else (GITE) operator. Consequently, we review the main algorithms used for verification techniques i.e. relational product and p...