algebraic operations
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1: 2.1 Definitions and Elementary Properties
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►means that for each , the difference between and the th partial sum on the right-hand side is as in .
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2: 18.38 Mathematical Applications
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►Algebraic structures were built of which special representations involve Dunkl type operators.
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►Much of the exploration of the EOP’s is based on the operator algebra as developed in SUSY, above.
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3: Bibliography K
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Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces.
Funktsional. Anal. i Prilozhen. 23 (1), pp. 24–40 (Russian).
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4: Errata
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►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions.
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5: DLMF Project News
error generating summary6: Bibliography T
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The universal Askey-Wilson algebra.
SIGMA 7, pp. Paper 069, 24 pp..
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The universal Askey-Wilson algebra and DAHA of type
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SIGMA 9, pp. Paper 047, 40 pp..
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Numerical Linear Algebra.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Dunkl shift operators and Bannai-Ito polynomials.
Adv. Math. 229 (4), pp. 2123–2158.
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Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves.
Trans. Amer. Math. Soc. 365 (12), pp. 6697–6729.
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7: 18.42 Software
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►Also included is a website (CAOP) operated by a university department.
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CAOP (website). Computer Algebra and Orthogonal Polynomials.
8: 26.19 Mathematical Applications
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►Combinatorics has applications to analysis, algebra, and geometry.
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►These have applications in operations research, probability theory, and statistics.
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9: 26.22 Software
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►Also included are websites operated by university departments and consortia, research institutions, and peer-reviewed journals.
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GAP (website). A system for computational discrete algebra.
Magma (website). A computational algebra system.
10: Bibliography D
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Computing spectra of linear operators using the Floquet-Fourier-Hill method.
J. Comput. Phys. 219 (1), pp. 296–321.
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Computing Riemann matrices of algebraic curves.
Phys. D 152/153, pp. 28–46.
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Abstract Algebra.
2nd edition, Prentice Hall Inc., Englewood Cliffs, N.J..
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Linear operators. Part II.
Wiley Classics Library, John Wiley & Sons, Inc., New York.
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Differential-difference operators associated to reflection groups.
Trans. Amer. Math. Soc. 311 (1), pp. 167–183.
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