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Sums of Entire Functions Having Only Real Zeros
| Content Provider | Semantic Scholar |
|---|---|
| Author | Adams, Steven R. Cardon, David A. |
| Copyright Year | 2006 |
| 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 or- thogonal polynomials. We discuss a similarity of this result with the Lee-Yang circle theorem from statistical mechanics. Also, we state several open prob- lems. |
| Starting Page | 3857 |
| Ending Page | 3866 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-07-09103-4 |
| Volume Number | 135 |
| Alternate Webpage(s) | https://math.byu.edu/~cardon/papers/SumsWithRealZeros.pdf |
| Alternate Webpage(s) | https://www.ams.org/journals/proc/2007-135-12/S0002-9939-07-09103-4/S0002-9939-07-09103-4.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0608297v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0608297v1.pdf |
| Alternate Webpage(s) | http://www.math.byu.edu/~cardon/papers/SumsWithRealZeros.pdf |
| Alternate Webpage(s) | https://math.byu.edu/~cardon/papers/SumsWithRealZerosProceedingsAMS.pdf |
| Alternate Webpage(s) | https://www.math.byu.edu/~cardon/papers/SumsWithRealZeros.pdf |
| Alternate Webpage(s) | http://www.math.byu.edu/~cardon/papers/SumsWithRealZerosProceedingsAMS.pdf |
| Alternate Webpage(s) | https://math.byu.edu/cardon/papers/SumsWithRealZerosProceedingsAMS.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-07-09103-4 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
