Cardinal spline interpolation : "Based on the ten lectures delivered at Northwestern University during the week of June 14 to 18, 1971, at the Regional Conference on 'Analysis with special emphasis on approximation theory'."

As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book - cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms. Cardinal Spline Interpolation......Page 3 Contents......Page 5 An Homage to Leonard Euler......Page 6 Preface......Page 7 Lecture 1 Introduction, Background and Examples......Page 9 Lecture 2 The Basis Property of B-Splines......Page 19 Lecture 3 The Exponential Euler Splines......Page 29 Lecture 4 Cardinal Spline Interpolation......Page 41 Lecture 5 Cardinal Hermite Interpolation......Page 51 Lecture 6 Other Spaces and Semi-Cardinal Interpolation......Page 67 Lecture 7 Finite Spline Interpolation Problems......Page 79 Lecture 8 Semi-Cardinal Interpolation and Quadratures with General Boundary Conditions......Page 93 Lecture 9 Extremum and Limit Properties......Page 103 Lecture 10 Applications: 1. Approximations of Fourier Transforms. 2. The Smoothing of Histograms......Page 117 References......Page 129 [by] I. J. Schoenberg. Based On The Ten Lectures Delivered At Northwestern University During The Week Of June 14 To 18, 1971, At The Regional Conference On 'analysis With Special Emphasis On Approximation Theory'. Bibliography: P. 121-125.