scholarly journals Simultaneous approximation of a uniformly bounded set of real valued functions

1985 ◽  
Vol 45 (2) ◽  
pp. 129-132
Author(s):  
Şermin Atacik
Keyword(s):  
Simultaneous Approximation ◽  
Bounded Set ◽  
Uniformly Bounded

scholarly journals The space of totally bounded analytic functions

1987 ◽  
Vol 30 (2) ◽  
pp. 229-246
Author(s):  
Alan L. Horwitz ◽  
Lee A. Rubel
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Sharp Bounds ◽  
Totally Bounded ◽  
Bounded Set ◽  
Inverse Interpolation ◽  
Derivatives Of ◽  
Uniformly Bounded

This paper is a continuation of our project on “inverse interpolation”, begun in [6]. In brief, the task of inverse interpolation is to deduce some property of a function f from some given property of the set L of its Lagrange interpolants. In the present work, the property of L is that it be a uniformly bounded set of functions when restricted to the domain of f. In particular (see Section 3), when the domain is a disc, we deduce sharp bounds on the successive derivatives of f. As a result, f must extend to be an analytic function (of restricted growth) in the concentric disc of thrice the original radius.

Bounded weight modules of the Lie algebra of vector fields on ℂ2

2017 ◽  
Vol 16 (12) ◽  
pp. 1750236 ◽  
Author(s):  
Andrew Cavaness ◽  
Dimitar Grantcharov
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Classification Result ◽  
New Family ◽  
Bounded Set ◽  
Tensor Formula ◽  
Uniformly Bounded ◽  
Weight Modules

We study weight modules of the Lie algebra [Formula: see text] of vector fields on [Formula: see text]. A classification of all simple weight modules of [Formula: see text] with a uniformly bounded set of weight multiplicities is provided. To achieve this classification, we introduce a new family of generalized tensor [Formula: see text]-modules. Our classification result is an important step in the classification of all simple weight [Formula: see text]-modules with finite weight multiplicities.

scholarly journals Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

2015 ◽  
Vol 14 (4) ◽  
pp. 41-51
Author(s):  
José Atilio Guerrero ◽  
◽  
Janusz Matkowski ◽  
Nelson Merentes ◽  
Małgorzata Wróbel ◽  
...  
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Functions Of Bounded Variation ◽  
Bounded Set ◽  
Uniformly Bounded

scholarly journals Some Conditions under Which Sequences of Functions are Uniformly Bounded

1968 ◽  
Vol 33 ◽  
pp. 75-83
Author(s):  
D.C. Rung
Keyword(s):  
Complex Analysis ◽  
Normal Family ◽  
Normal Families ◽  
Usual Pattern ◽  
Uniformly Bounded

After one introduces the theory of normal families in a course in complex analysis, the usual pattern is to give an example of a non-normal family. One of the simplest, of course, is the sequence fn(z) = nz, n = 1,2, ···. The very devastating effect of multiplying by zero insures the required abnormality!

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

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