• Publications
  • Influence
Bases in Banach Spaces II
Vol. II. Chapter III. Generalizations of the Notion of a Basis.- 0. Banach spaces which do not have the approximation property.- I. Countable Generalizations of Bases.- 1. Basic sequences. BibasicExpand
  • 675
  • 39
Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces
espace lineaire norme # espace metrique # meilleure approximation # sous-espace lineaire # sous-espace lineaire de dimension finie # sous-espace lineaire ferme de codimension finie # elementExpand
  • 713
  • 24
Abstract Convex Analysis
Abstract Convexity of Elements of a Complete Lattice. Abstract Convexity of Subsets of a Set. Abstract Convexity of Functions on a Set. Abstract Quasi-Convexity of Functions on a Set. DualitiesExpand
  • 281
  • 24
Topical and sub-topical functions, downward sets and abstract convexity
We study topical and sub-topical functions (i.e., functions which are increasing in the natural partial ordering of ℝn and additively homogeneous, respectively additively sub-homogeneous), andExpand
  • 81
  • 12
High-order finite difference methods for the Helmholtz equation
High-order finite difference methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids. The standard pointwise representation has aExpand
  • 150
  • 9
Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities
We introduce and study the Abadie constraint qualification, the weak Pshenichnyi--Levin--Valadier property, and related constraint qualifications for semi-infinite systems of convex inequalities and linear inequalities. Expand
  • 83
  • 8
We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncationExpand
  • 65
  • 8
  • PDF
Best Approximation by Normal and Conormal Sets
The aim of the present paper is to develop a theory of best approximation by elements of so-called normal sets and their complements-conormal sets-in the non-negative orthant R^I"+ of aExpand
  • 35
  • 6
Downward Sets and their separation and approximation properties
We develop a theory of downward subsets of the space ℝI, where I is a finite index set and T is an arbitrary index set, and we give some characterizations of best approximations by downward sets. Expand
  • 60
  • 4