Volume 3,  Issue 3, 2002

Article 39

ITERATED LAGUERRE AND TURÁN INEQUALITIES

THOMAS CRAVEN AND GEORGE CSORDAS

DEPARTMENT OF MATHEMATICS,
UNIVERSITY OF HAWAII,
 HONOLULU, HI 96822
E-Mail: tom@math.hawaii.edu

E-Mail: george@math.hawaii.edu

Received 12 September, 2001; Accepted 15 March, 2002.
Communicated by: K.B. Stolarsky


ABSTRACT.   New inequalities are investigated for real entire functions in the Laguerre-Pólya class. These are generalizations of the classical Turán and Laguerre inequalities. They provide necessary conditions for certain real entire functions to have only real zeros.
Key words:
Laguerre-Pólya class, Multiplier sequence, Hankel matrix, Real zeros.

2000 Mathematics Subject Classification:
Primary 26D05; Secondary 26C10, 30C15.


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