On the multiplicities of the zeros of laguerre-pólya functions

Joe Kamimoto, Haseo Ki, Young One Kim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We show that all the zeros of the Fourier transforms of the functions exp(-x2m), m = 1,2,⋯, are real and simple. Then, using this result, we show that there are infinitely many polynomials p(x1,⋯, xn) such that for each (m1,⋯, mn) ∈ (ℕ \ {0})n the translates of the function p(x1,⋯, xn)exp (-∑j=1nxj2mj) generate L1(ℝn). Finally, we discuss the problem of finding the minimum number of monomials pα(x1,⋯, xn), α ∈ A, which have the property that the translates of the functions pα(x1,⋯, xn)exp(-∑j=1nxj2mj), α ∈ A, generate L1n), for a given (m1,⋯,mn) ∈ (ℕ\{0})n.

Original languageEnglish
Pages (from-to)189-194
Number of pages6
JournalProceedings of the American Mathematical Society
Volume128
Issue number1
DOIs
Publication statusPublished - 2000

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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