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Sums of entire functions having only real zeros
Author(s):
Steven
R.
Adams;
David
A.
Cardon
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3857-3866.
MSC (2000):
Primary 30C15;
Secondary 30D05
Posted:
August 29, 2007
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Abstract:
We show that certain sums of products of Hermite-Biehler entire functions have only real zeros, extending results of Cardon. As applications of this theorem, we construct sums of exponential functions having only real zeros, we construct polynomials having zeros only on the unit circle, and we obtain the three-term recurrence relation for an arbitrary family of real orthogonal polynomials. We discuss a similarity of this result with the Lee-Yang Circle Theorem from statistical mechanics. Also, we state several open problems.
References:
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Additional Information:
Steven
R.
Adams
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
David
A.
Cardon
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
cardon@math.byu.edu
DOI:
10.1090/S0002-9939-07-09103-4
PII:
S 0002-9939(07)09103-4
Received by editor(s):
August 9, 2006
Posted:
August 29, 2007
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2007,
American Mathematical Society
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