scholarly journals Conditions of unicity of the best non-symmetric $L_1$-approximant for continuous vector-valued functions by one-dimensional subspace

2012 ◽  
Vol 20 ◽  
pp. 129
Author(s):  
M.Ye. Tkachenko ◽  
V.M. Traktyns'ka
Keyword(s):  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Necessary And Sufficient Conditions ◽  
Continuous Vector ◽  
One Dimensional ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha};\overline{\beta})$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

scholarly journals Conditions of unicity of the best non-symmetric $L_1$-approximant

2013 ◽  
Vol 21 ◽  
pp. 81
Author(s):  
Yu.S. Zagorul'ko ◽  
M.Ye. Tkachenko ◽  
V.M. Traktyns'ka
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuous Vector ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha},\overline{\beta})$-approximant with coefficient constraints for the continuous vector-valued functions on a metric compact are obtained.

scholarly journals Conditions of unicity of the best nonsymmetric $L_1$-approximant for vector-valued functions by one-dimensional subspace

2021 ◽  
Vol 19 ◽  
pp. 123
Author(s):  
M.Ye. Tkachenko ◽  
V.M. Traktynska
Keyword(s):  
Dimensional Subspace ◽  
Continuous Vector ◽  
One Dimensional ◽  
Vector Valued Functions ◽  
Vector Valued

The conditions of the unicity of the best nonsymmetric $L_1$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

On continuity properties of some classes of vector-valued functions

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
K. Naralenkov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuity Properties ◽  
Weakly Continuous ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractWe extend the V BG* property to the context of vector-valued functions and give some characterizations of this property. Necessary and sufficient conditions for vector-valued VBG* functions to be continuous or weakly continuous, except at most on a countable set, are obtained.

The order completeness of some spaces of vector-valued functions

1974 ◽  
Vol 11 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Donald I. Cartwright
Keyword(s):  
Banach Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Banach Lattices ◽  
Nuclear Operators ◽  
Order Completeness ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Order Intervals ◽  
Vector Valued

Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.

Analogs of Fricke's theorems for analytic vector-valued functions in the unit ball having bounded L-index in joint variables.

2019 ◽  
Vol 33 ◽  
pp. 16-26 ◽  
Author(s):  
Vitalina Baksa ◽  
Andriy Bandura ◽  
Oleg Skaskiv
Keyword(s):  
Unit Ball ◽  
Vector Function ◽  
Sufficient Conditions ◽  
Maximum Modulus ◽  
Function Class ◽  
Analytic Vector ◽  
Continuous Vector ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, we present necessary and sufficient conditions of boundedness of $\mathbb{L}$-index in joint variables for vector-functions analytic in the unit ball, where $\mathbf{L}=(l_1,l_2): \mathbb{B}^2\to\mathbb{R}^2_+$ is a positive continuous vector-function, $\mathbb{B}^2=\{z\in\mathbb{C}^2: |z|=\sqrt{|z_1|^2+|z_2|^2}\le 1\}.$ Particularly, we deduce analog of Fricke's theorems for this function class, give estimate of maximum modulus on the skeleton of bidisc. The first theorem concerns sufficient conditions. In this theorem we assume existence of some radii, for which the maximum of norm of vector-function on the skeleton of bidisc with larger radius does not exceed maximum of norm of vector-function on the skeleton of bidisc with lesser radius multiplied by some costant depending only on these radii. In the second theorem we show that boundedness of $\mathbf{L}$-index in joint variables implies validity of the mentioned estimate for all radii.

GENERALIZED DECIMATION INVARIANT SEQUENCES IN DIMENSION N

2002 ◽  
Vol 12 (04) ◽  
pp. 709-737 ◽  
Author(s):  
A. BARBÉ ◽  
F. VON HAESELER
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
One Dimensional ◽  
Necessary And Sufficient

We generalize the concept of one-dimensional decimation invariant sequences, i.e. sequences which are invariant under a specific rescaling, to dimension N. After discussing the elementary properties of decimation-invariant sequences, we focus our interest on their periodicity. Necessary and sufficient conditions for the existence of periodic decimation invariant sequences are presented.

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