The theory of approximation

Title page
Preface
CHAFTER I: CONTINUOUS FUNCTIONS
Introduction
1. Approximation by trigonometric sums
2. Approximation by polynomials
3. Degree of convergence of Fourier series
4. Degree of convergence of Legendre series
CHAPTER II: DISCONTINUOUS FUNCTIONS; FUNCTIONS OF LIMITED VARIATION; ARITHMETIC MEANS
Introduction
1. Convergence of Fourier series under hypothesis of continuity over part of a period
2. Convergence of Fourier series under hypothesis of limited variation
3. Degree of convergence of Fourier series under hypotheses involving limited variation
4. Convergence of the first arithmetic mean
5. Degree of convergence of the first arithmetic mean
6. Convergence of Legendre series under hypothesis of continuity over a part of the interval
7. Degree of convergence of Legendre series under hypotheses involving limited variation
CHAPTER III: THE PRINCIPLE OF LEAST SQUARES AND ITS GENERALIZATIONS
1. Convergence of trigonometric approximation as related to integral of square of error
2. Convergence of trigonometric approximation as related to integral of mth power of error
3. Proof of an existence theorem
4. Polynomial approximaximation
5. Polynomial approximation over an infinite interval
CHAPTER IV: TRIGONOMETRIC INTERPOLATION
1. Fundamental formulas of trigonometric interpolation
2. Convergence and degree of convergence under hypotheses of continuity over entire period
3. Convergence under hypothesis of continuity over part of a period
4. Convergence under hypothesis of limited variation
5. Degree of convergence under hypotheses involving limited variation
6. Formula of interpolation analogous to the Fejér mean
7. Polynomial interpolation
CHAPTER V: INTRODUCTION TO THE GEOMETRY OF FUNCTION SPACE
1. The notions of distance and orthogonality
2. The general notion of angle; geometric interpretation of coefficients of correlation
3. Coefficients of correlation in an arbitrary number of variables
4. The geometry of frequency functions
5. Vector analysis in function space