The present paper is, in spirit, a sequel to [5], but may be read independently of that paper. The underlying motive is to provide a satisfactory, and suitably quantitative, theory of “degree of approximation” for functions of several variables. In this section we discuss some ramifications of this general problem, and outline a program of investigation, of which some first steps are carried out in the following sections. Although, or perhaps because, our results are quite fragmentary, we hope they might stimulate interest in the present circle of questions.


Linear Functional Absolute Constant Tauberian Theorem Underlying Motive Mild Limit 
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Copyright information

© Springer Basel AG 1969

Authors and Affiliations

  • Harold S. Shapiro
    • 1
  1. 1.Dept. of Math.University of MichiganUSA

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