orthogonal invariance
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1: 35.4 Partitions and Zonal Polynomials
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Orthogonal Invariance
…2: 35.7 Gaussian Hypergeometric Function of Matrix Argument
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§35.7(iii) Partial Differential Equations
…3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
4: Bille C. Carlson
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►In theoretical physics he is known for the “Carlson-Keller Orthogonalization”, published in 1957, Orthogonalization Procedures and the Localization of Wannier Functions, and the “Carlson-Keller Theorem”, published in 1961, Eigenvalues of Density Matrices.
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►This invariance usually replaces sets of twelve equations by sets of three equations and applies also to the relation between the first symmetric elliptic integral and the Jacobian functions.
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5: Bibliography D
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical
Sciences, New York.
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Strong asymptotics of orthogonal polynomials with respect to exponential weights.
Comm. Pure Appl. Math. 52 (12), pp. 1491–1552.
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Sharp bounds for the extreme zeros of classical orthogonal polynomials.
J. Approx. Theory 162 (10), pp. 1793–1804.
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Inequalities for extreme zeros of some classical orthogonal and -orthogonal polynomials.
Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
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Supersymmetry, shape invariance, and exactly solvable potentials.
Amer. J. Phys. 56, pp. 163–168.
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6: Bibliography
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Some orthogonal
-polynomials.
Math. Nachr. 30, pp. 47–61.
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Characterization theorems for orthogonal polynomials.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 1–24.
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A trinomial analogue of Bailey’s lemma and superconformal invariance.
Comm. Math. Phys. 192 (2), pp. 245–260.
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Classical Orthogonal Polynomials.
In Orthogonal Polynomials and Applications, C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux (Eds.),
Lecture Notes in Math., Vol. 1171, pp. 36–62.
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Recurrence relations, continued fractions, and orthogonal polynomials.
Mem. Amer. Math. Soc. 49 (300), pp. iv+108.
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7: Bibliography B
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Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
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Normalization integrals of orthogonal Heun functions.
J. Math. Phys. 38 (7), pp. 3692–3699.
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Orthogonality relations for the associated Legendre functions of imaginary order.
Integral Transforms Spec. Funct. 24 (4), pp. 331–337.
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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Density profiles in confined critical systems and conformal invariance.
Phys. Rev. Lett. 66 (7), pp. 895–898.
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