| Title:
|
Generalizations of the classical Chebyshev polynomials to polynomials in two variables (English) |
| Author:
|
Dunn, Ken B. |
| Author:
|
Lidl, Rudolf |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1982 |
| Pages:
|
516-528 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
33A65 |
| idZBL:
|
Zbl 0511.33008 |
| idMR:
|
MR682129 |
| DOI:
|
10.21136/CMJ.1982.101831 |
| . |
| Date available:
|
2008-06-09T14:50:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101831 |
| . |
| Reference:
|
[1] T. Bang: Congruence properties of Tchebycheff polynomials.Math. Scand., v. 2, 1954, pp. 327-333. Zbl 0057.28301, MR 0067130, 10.7146/math.scand.a-10418 |
| Reference:
|
[2] B. M. Dankovič: Orttiogonal polynomials in several variables.private communication, 1974. |
| Reference:
|
[3] L. E. Dickson: Linear Groups With An Exposition Of Galois Field Theory.New York, Dover, 1958. MR 0104735 |
| Reference:
|
[4] R. Eier, R. Lidl: Tschebycheffpolynome in einer und zwei Variablen.Abh. Math. Sem. Univ. Hamburg, v. 41, 1974, pp. 17-27. MR 0344546, 10.1007/BF02993497 |
| Reference:
|
[5] A. Erdélyi W. Magnus F. Oberhettinger F. G. Tricomi: Higher Transcendental Functions.v. II, McGraw-Hill, New York, 1953. MR 0058756 |
| Reference:
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[6] M. Fried: On a conjecture of Schur.Michigan Math. J., v. 17, 1970, pp. 41 - 55. Zbl 0169.37702, MR 0257033, 10.1307/mmj/1029000374 |
| Reference:
|
[7] R. O. Hays: Multi-dimensional extensions of the Chebyshev polynomials.Math. Соmр., v. 27, 1973, pp. 621-624. Zbl 0281.65011, MR 0333526 |
| Reference:
|
[8] H. K. Kaiser, R. Lidl: Die Polynomlösungen spezieller partieller Differentialgleichungen.Monatsh. Math., v. 81, 1976, pp. 109-111. Zbl 0364.33013, MR 0396505, 10.1007/BF01301235 |
| Reference:
|
[9] T. H. Koornwinder: Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, I, II.Nederl. Akad. Wetensch. Proc. Ser A77 = Jndag. Math., v. 36, 1974, pp. 48 - 66. Zbl 0267.33008, MR 0340673, 10.1016/1385-7258(74)90013-4 |
| Reference:
|
[10] T. H. Koornwinder: Orthogonal polynomials in two variables which are eigenfunction of two algebraically independent partial differential operators, III, lV.Nederl. Akad. Wetensch. Proc. Ser. A77 = Jndag. Math., v. 36, 1974, pp. 357-381. MR 0357905, 10.1016/1385-7258(74)90026-2 |
| Reference:
|
[11] T. H. Koornwinder: Two-variable analogues of the classical orthogonal polynomials.in Theory And Application Of Special Functions, (R. Askey, ed.), pp. 435 - 495, Academic Press, New York, 1975. Zbl 0326.33002, MR 0402146 |
| Reference:
|
[12] H. Lausch W. Nöbauer: Algebra Of Polynomials.North Holland, Amsterdam, 1973. MR 0349544 |
| Reference:
|
[13] R. Lidl С. Wells: Chebyshev polynomials in several variables.J. Reine Angew. Math., v. 255, 1972, рр. 104-111. MR 0306164 |
| Reference:
|
[14] R. Lidl: Tschebyscheffpolynome und die dadurch dargestellten Gruppen.Monatsh. Math., v. 77, 1973, pp. 132-147. Zbl 0257.12011, MR 0318106, 10.1007/BF01295046 |
| Reference:
|
[15] R. Lidl: Tschebyscheffpolynome in mehreren Variablen.J. Reine Angew. Math., v. 273, 1975, pp. 178-198. Zbl 0298.33009, MR 0364200 |
| Reference:
|
[16] R. A. Rankin: Chebyshev polynomials and the modulary group of level $p$.Math. Scand., V. 2, 1954, pp. 315-326. MR 0067154 |
| Reference:
|
[17] P. E. Ricci: I polinomi di Tchebycheff in più variabili.Rend. Di Matem. v. 11, 1978, pp. 295-327. Zbl 0405.15012 |
| Reference:
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[18] T. J. Rivlin: The Chebyshev Polynomials.John Wiley & Sons, New York, 1974. Zbl 0299.41015, MR 0450850 |
| Reference:
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[19] I. Schur: Gesammelte Abhandlungen.v. 3, Springer Verlag, Berlin, 1973. Zbl 0274.01054 |
| Reference:
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[20] G. Szegö: Orthogonal Polynomials.A.M.S. Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1967. MR 0310533 |
| Reference:
|
[21] K. B. Dunn R. Lidl: Multi-dimensional generalization of the Chebyshev polynomials, I, II.Proc. Japan Acad. 56, 1980, pp. 154-165. MR 0575995 |
| Reference:
|
[22] R. Eier R. Lidl K. B. Dunn: Differential equations for generalized Chebyshev polynomials.Rendi di Matem. 1, 1981, pp. 633-646. MR 0647460 |
| Reference:
|
[23] R. Eier R. Lidl: A class of orthogonal polynomials in $k$ variables.Math. Ann. 260, 1982, pp. 93-99. MR 0664368, 10.1007/BF01475757 |
| . |
