Spaces of Approximating Functions with Haar-like Conditions
Kitahara, Kazuaki.
Spaces of Approximating Functions with Haar-like Conditions [electronic resource] / by Kazuaki Kitahara. - VIII, 110 p. online resource. - Lecture Notes in Mathematics, 1576 0075-8434 ; . - Lecture Notes in Mathematics, 1576 .
Preliminaries -- Characterizations of approximating spaces of C[a, b] or C 0(Q) -- Some topics of haar-like spaces of F[a, b] -- Approximation by vector-valued monotone increasing or convex functions -- Approximation by step functions.
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions. It studies topics of subclasses of Haar-like spaces, that is, classes of Tchebycheff or weak Tchebycheff spaces, spaces of vector-valued monotone increasing or convex functions and spaces of step functions. The notion of Haar-like spaces provides a general point of view which includes the theories of approximation from the above spaces. The contents are largely new. Graduate students and researchers in approximation theory will be able to read this book with only basic knowledge of analysis, functional analysis and linear algebra.
9783540484042
10.1007/BFb0091385 doi
Mathematics.
Real Functions.
QA331.5
515.8
Spaces of Approximating Functions with Haar-like Conditions [electronic resource] / by Kazuaki Kitahara. - VIII, 110 p. online resource. - Lecture Notes in Mathematics, 1576 0075-8434 ; . - Lecture Notes in Mathematics, 1576 .
Preliminaries -- Characterizations of approximating spaces of C[a, b] or C 0(Q) -- Some topics of haar-like spaces of F[a, b] -- Approximation by vector-valued monotone increasing or convex functions -- Approximation by step functions.
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions. It studies topics of subclasses of Haar-like spaces, that is, classes of Tchebycheff or weak Tchebycheff spaces, spaces of vector-valued monotone increasing or convex functions and spaces of step functions. The notion of Haar-like spaces provides a general point of view which includes the theories of approximation from the above spaces. The contents are largely new. Graduate students and researchers in approximation theory will be able to read this book with only basic knowledge of analysis, functional analysis and linear algebra.
9783540484042
10.1007/BFb0091385 doi
Mathematics.
Real Functions.
QA331.5
515.8