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Spectral Problems for the Dirac System with Spectral Parameter in Local Boundary Conditions

On the Structure of the Complements of Chebyshev Sets

A Generalized Implicit Function Theorem

On Polytopes that are Simple at the Edges

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The Fermion Model of Representations of Affine Krichever–Novikov Algebras

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Towards the Definition of Generalized Chebyshev Polynomials over Finite Fields

Ultraspectra of a Representation of a Banach Lie Algebra

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On the Rubel–Taylor Problem on a Representation of Holomorphic Functions

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On the Structure of the Complements of Chebyshev Sets

Content Provider	Springer Nature Link
Author	Alimov, A. R.
Copyright Year	2001
Abstract	A set is called a Chebyshev set if it contains a unique best approximation element. We study the structure of the complements of Chebyshev sets, in particular considering the following question: How many connected components can the complement of a Chebyshev set in a finite-dimensional normed or nonsymmetrically normed linear space have? We extend some results from [A. R. Alimov, East J. Approx, 2, No. 2, 215--232 (1996)]. A. L. Brown's characterization of four-dimensional normed linear spaces in which every Chebyshev set is convex is extended to the nonsymmetric setting. A characterization of finite-dimensional spaces that contain a strict sun whose complement has a given number of connected components is established.
Starting Page	176
Ending Page	182
Page Count	7
File Format	PDF
ISSN	00162663
Journal	Functional Analysis and Its Applications
Volume Number	35
Issue Number	3
e-ISSN	15738485
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2001-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Functional Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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The geometric structure of Chebyshev sets in ℓ∞(n)

Chebyshev Polynomials on Generalized Julia Sets

Locally Chebyshev sets on the plane

Towards the Definition of Generalized Chebyshev Polynomials over Finite Fields

Chebyshev Polynomials on Compact Sets

Convexity of Chebyshev Sets in Hilbert Spaces

On remotality for convex sets in Banach spaces

Exponential analytic sets

Convexity of 2-Chebyshev sets in Hilbert space

On the Structure of the Complements of Chebyshev Sets

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