NDLI: New Moduli of Smoothness on the Unit Ball and Other Domains, Introduction and Main Properties

Content Provider	Springer Nature Link
Author	Ditzian, Z.
Copyright Year	2014
Abstract	A new set of moduli of smoothness on a large variety of Banach spaces of functions on the unit ball is introduced. These measures of smoothness utilize uniformly bounded holomorphic semigroups on the Banach space in question. The new moduli are “correct” in the sense that they satisfy direct (Jackson) and weak converse inequalities. The method used also applies to spaces of functions on the simplex and the unit sphere, and while the main goal is the investigation of properties and relations concerning the unit ball, many of the results will be given for other domains and situations. The classic properties, including equivalence with appropriate $$K$$ -functionals or realization functionals, will be established. Bernstein- and Kolmogorov-type inequalities are proved.
Ending Page	36
Page Count	36
Starting Page	1
File Format	PDF
ISSN	01764276
e-ISSN	14320940
Journal	Constructive Approximation
Issue Number	1
Volume Number	40
Language	English
Publisher	Springer US
Publisher Date	2014-04-22
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inequalities in approximation (Bernstein, Jackson, Nikol'skiÄ-type inequalities) Inverse theorems Approximation by positive operators Moduli of smoothness Orthogonal expansion Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) Multidimensional problems (should also be assigned at least one other classification number in this section) Holomorphic semigroups Realization functionals Approximation by polynomials Sphere and simplex Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Numerical Analysis Analysis $$K$$ -Functionals Function spaces on the unit ball Best approximation Groups and semigroups of linear operators Special properties of functions of several variables, HÃ¶lder conditions, etc.
Content Type	Text
Resource Type	Article
Subject	Analysis Computational Mathematics

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