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References
ASKEY, R., Jacobi polynomials, I. New proofs of Koornwinder's Laplace type integral representation and Bateman's bilinear sum, SIAM J. Math. Anal 5 (1974), 119–124.
BAVINCK, H., Jacobi series and approximation, Mathematical Centre Tracts, No. 39, Mathematisch Centrum, Amsterdam, 1972.
BAVINCK, H., Convolution operators for Fourier-Jacobi expansions, in "LInear operators and approximation" (P.L. Butzer, J.-P. Kahane & B. Sz.-Nagy, eds.), p. 371–380, ISNM Vol. 20, Birkhäuser-Verlag, Basel, 1972.
BOCHNER, S., Uber Sturm-Liouvillesche Polynomsysteme, Math. Z. 29 (1929), 730–736.
ERDÉLYI, A., W. MAGNUS, F. OBERHETTINGER & F.G. TRICOMI, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, 1953.
GANGOLLI, R., Positive definite kernels on homogeneous spaces and certain stochastic processes related to Levy's Brownian motion of several parameters, Ann. Inst. H. Poincaré sect. B (N.S.) 3 (1967), 121–226.
GELBART, S., A theory of Stiefel harmonics, Trans. Amer. Math. Soc. 192 (1974), 29–50.
HARISH-CHANDRA, Spherical functions on a semi-simple Lie group, I, Amer. J. Math. 80 (1958), 241–310.
HELGASON, S., The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153–180.
JAMES, A.T., Normal multivariate analysis and the orthogonal group, Ann. Math. Statist. 25 (1954), 40–75.
JAMES, A.T. & A.G. CONSTANTINE, Generalized Jacobi polynomials as spherical functions of the Grassmann manifold, Proc. London Math. Soc. (3) 29 (1974), 174–192.
KOORNWINDER, T.H., Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators, I, II, Nederl. Akad. Wetensch. Proc. Ser. A 77 = Indag. Math. 36 (1974), 59–66.
KOORWINDER, T.H., 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.
KOORNWINDER, T.H. & I.G. SPRINKHUIZEN, Generalized power series expansions for a class of orthogonal polynomials in two variables, Math. Centrum, Amsterdam, Report TW 155 (1976).
LEVINE, D.A., Systems of singular integral operators on spheres, Trans. Amer. Math. Soc. 144 (1969), 493–521.
MAASS, H., Zur Theorie der Kugelfunktionen einer Matrixvariabelen, Math. Ann. 135 (1958), 391–416.
SPRINKHUIZEN, I.G., Orthogonal polynomials in two variables. A further analysis of the polynomials orthogonal over a region bounded by two lines and a parabola, Math. Centrum, Amsterdam, Report TW 144 (1974), also to appear in SIAM J. Math. Anal.
STRICHARTZ, R., The explicit Fourier decomposition of L2(SO(n)/SO(n-m)), Canad. J. Math. 27 (1975), 294–310.
SZEGÓ, G., Orthogonal polynomials, A.M.S. Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., Third ed., 1967.
TON-THAT, T., Lie group representations and harmonic polynomials of a matrix variable, Trans. Amer. Math. Soc. 216 (1976), 1–46.
VRETARE, L., Elementary spherical functions on symmetric spaces, Ark. Mat., to appear.
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Koornwinder, T. (1977). Harmonics and spherical functions on Grassmann manifolds of rank two and two-variable analogues of Jacobi polynomials. In: Schempp, W., Zeller, K. (eds) Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086570
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DOI: https://doi.org/10.1007/BFb0086570
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