On the multiplicities of the zeros

of Laguerre-Pólya functions

Authors:
Joe Kamimoto, Haseo Ki and Young-One Kim

Journal:
Proc. Amer. Math. Soc. **128** (2000), 189-194

MSC (1991):
Primary 30D15, 30D35, 41A30, 43A20

DOI:
https://doi.org/10.1090/S0002-9939-99-04970-9

Published electronically:
June 21, 1999

MathSciNet review:
1616650

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that all the zeros of the Fourier transforms of the functions , , are real and simple. Then, using this result, we show that there are infinitely many polynomials such that for each the translates of the function

generate . Finally, we discuss the problem of finding the minimum number of monomials , , which have the property that the translates of the functions , , generate , for a given .

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Additional Information

**Joe Kamimoto**

Affiliation:
Department of Mathematics, Kumamoto University, Kumamoto 860, Japan

Email:
joe@sci.kumamoto-u.ac.jp

**Haseo Ki**

Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749, Korea

Email:
haseo@bubble.yonsei.ac.kr

**Young-One Kim**

Affiliation:
Department of Mathematics, Sejong University, Seoul 143–747, Korea

Email:
kimyo@kunja.sejong.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-99-04970-9

Keywords:
Fourier transform,
Laguerre--P\'{o}lya function,
Wiener's theorem

Received by editor(s):
February 2, 1998

Received by editor(s) in revised form:
March 16, 1998

Published electronically:
June 21, 1999

Additional Notes:
The first author was partially supported by Grant-in-Aid for Scientific Research (No. 10740073), Ministry of Education, Science and Culture, Japan

The second author was supported by Yonsei University Research Fund of 1998

The third author was supported by the Korea Science and Engineering Foundation(KOSEF) through the Global Analysis Research Center(GARC) at Seoul National University.

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 1999
American Mathematical Society