unit ball

unit ball

[′yü·nət ′bȯl]
(mathematics)
The set of all points in euclidean n-space whose distance from the origin is at most 1.
Mentioned in ?
References in periodicals archive ?
The open ball {z [member of] [C.sup.n]: ||z|| < r} is denoted by [B.sub.r.sup.n] and the unit ball [B.sub.1.sup.n] by [B.sup.n].
When [omega](t) = t, Li and Wulan [8] obtained the analogues of Theorems 3.7 and 3.8 for holomorphic Bloch space on the unit ball of [C.sup.n].
Unlike the case of the unit ball (see [5]), the above result can not be deduced from the boundedness of the families of Bergman-type operators considered in [2, 6].
extended the Roper-Suffridge operator on the unit ball in [C.sup.n] and proved the extended operator preserves star-likeness and convexity if and only if some conditions are satisfied in [6].
It would be indeed nice and convenient if such a symmetry always existed, given its implications on the geometry of the unit ball of X.
Tenders are invited for Auto Valve Unit Ball Type To Escorts Part No.6355
To prove that a Lispchitz-free space is not isometric to [l.sub.1], we will exhibit two extreme points of its unit ball at distance less than one.
The 24 papers here consider such topics as characterizing holomorphic and meromorphic functions using maximum principles, generalizing trigonometric functions from different points of view, amenability as a hereditary property in some algebras of vector-valued functions, weighted composition operators on weighted sequence spaces, and the essential norm of operators on the Bergman space of vector-valued functions on the unit ball. ([umlaut] Ringgold, Inc., Portland, OR)
Figueiredo and Fonesca [6] solved a different version of the MostPoints(P, 1) problem: Given a set of n points with positive real weights in d-dimensional space, they consider an approximation to the problem of placing a unit ball, such that the sum of the weights of the points enclosed by the ball is maximized.
For a Banach space X, its dual space is denoted by [X.sup.*], [B.sub.X] is the closed unit ball of X, and [S.sub.X] stands for the unit sphere of X.
During the luncheon, there will be a raffle to raise money to fund the unit ball; to purchase a new scanner for the FRG office; and to purchase supplies for an orphanage in Afghanistan informally adopted by the brigade during their deployment.