The boundedness of orthonormal polynomials on certain curves of the fourth degree

Author:
Dunham Jackson

Journal:
Trans. Amer. Math. Soc. **63** (1948), 193-206

MSC:
Primary 41.1X

DOI:
https://doi.org/10.1090/S0002-9947-1948-0023956-1

MathSciNet review:
0023956

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References | Similar Articles | Additional Information

**[1]**D. Jackson,*Orthogonal trigonometric sums*, Ann. of Math. (2) vol. 34 (1933) pp. 799-814. MR**1503134****[2]**-,*Orthogonal polynomials on a plane curve*, Duke Math. J. vol. 3 (1937) pp. 228-236. MR**1545982****[3]**-,*Polynomial approximation on a curve of the fourth degree*, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 388-393. MR**1563548****[4]**-,*Orthogonal polynomials with auxiliary conditions*, Trans. Amer. Math. Soc. vol. 48 (1940) pp. 72-81. MR**0002684 (2:98f)****[5]**-,*Fourier series and orthogonal polynomials*, Carus Monograph Series, no. 6, 1941. MR**0005912 (3:230f)****[6]**-,*Generalization of a theorem of Korous on the bounds of orthonormal polynomials*, Bull. Amer. Math. Soc. vol. 48 (1942) pp. 602-608. MR**0006784 (4:41e)****[7]**-,*Boundedness of orthonormal polynomials on loci of the second degree*, Duke Math. J. vol. 11 (1944) pp. 351-365. MR**0010735 (6:62c)****[8]**-,*Boundedness of orthonormal polynomials in one, two, and three variables*, Trans. Amer. Math. Soc. vol. 58 (1945) pp. 167-183. MR**0012719 (7:64c)****[9]**-,*The boundedness of orthonormal polynomials on certain curves of the third degree*, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 899-907. MR**0017446 (8:155b)****[10]**F. Koehler,*Systems of orthogonal polynomials on certain algebraic curves*, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 345-351. MR**0003287 (2:194g)****[11]**Margaret Martin,*Some new systems of orthogonal polynomials on algebraic curves*, Thesis, University of Minnesota, not yet published.**[12]**G. Szegö,*Orthogonal polynomials*, Amer. Math. Soc. Colloquium Publications, vol. 23, 1939.

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DOI:
https://doi.org/10.1090/S0002-9947-1948-0023956-1

Article copyright:
© Copyright 1948
American Mathematical Society