| Title:
|
Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation (English) |
| Author:
|
Ndikubwayo, Innocent |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
793-804 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\{P_i\}_{i=1}^{\infty }$ generated by a three-term recurrence relation $P_i(x)+ Q_1(x)P_{i-1}(x) +Q_2(x) P_{i-2}(x)=0$ with the standard initial conditions $P_{0}(x)=1, P_{-1}(x)=0,$ where $Q_1(x)$ and $Q_2(x)$ are arbitrary real polynomials. (English) |
| Keyword:
|
recurrence relation |
| Keyword:
|
polynomial sequence |
| Keyword:
|
support |
| Keyword:
|
real zeros |
| MSC:
|
12D10 |
| MSC:
|
26C10 |
| MSC:
|
30C15 |
| idZBL:
|
07250690 |
| idMR:
|
MR4151706 |
| DOI:
|
10.21136/CMJ.2020.0535-18 |
| . |
| Date available:
|
2020-09-07T09:39:33Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148329 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Kostov, V. P., Shapiro, B., Tyaglov, M.: Maximal univalent disks of real rational functions and Hermite-Biehler polynomials.Proc. Am. Math. Soc. 139 (2011), 1625-1635. Zbl 1223.26033, MR 2763752, 10.1090/S0002-9939-2010-10778-5 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
