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  • E Hille
  • Proceedings of the National Academy of Sciences…
  • 1969
A study has been made of some mathematical aspects of the Thomas-Fermi equation. This is a preliminary report on the results obtained, including (1) convergence of relevant series, (2) existence of unbounded solutions, (3) existence of solutions having an arbitrary branch point, (4) determination of a class of solutions bounded for large values of the(More)
Such families arise in the most varied branches of classical and of modern analysis and are interesting for their own sake as well as for the many applications. An extension to the w-parameter case was presented to the Society in October 1944 (abstract 51-1-15). Here the parameter a = (au ai, • • • , an) is a vector in ^-dimensional real euclidean space En,(More)
  • E Hille
  • Proceedings of the National Academy of Sciences…
  • 1944
1. Recently I. Gelfand1 has defined a class of characters of Abelian groups embedded in a normed commutative vector ring. The present note contains an elaboration of this theory with a strengthening of the main theorem and extensions to semi-groups. Let 9R be a normed commutative vector ring with unit element e, £ the set of maximal ideals 9 in 9?, 9/9) the(More)