x-difference%20operators
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1—10 of 174 matching pages
1: William P. Reinhardt
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►Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
2: 20 Theta Functions
Chapter 20 Theta Functions
…3: 3.4 Differentiation
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Biharmonic Operator
… ►Those for the Laplacian and the biharmonic operator follow from the formulas for the partial derivatives. …4: Bibliography K
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Lowering and Raising Operators for Some Special Orthogonal Polynomials.
In Jack, Hall-Littlewood and Macdonald Polynomials,
Contemp. Math., Vol. 417, pp. 227–238.
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator.
Adv. Math. 333, pp. 796–821.
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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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Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions.
J. Math. Anal. Appl. 324 (1), pp. 285–303.
5: 14.30 Spherical and Spheroidal Harmonics
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Parity Operation
… ►Here, in spherical coordinates, is the squared angular momentum operator: ►
14.30.12
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component of the angular momentum operator
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14.30.13
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6: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators.
Academic Press, New York.
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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators.
Z. Angew. Math. Mech. 78 (1), pp. 66–72.
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On the foundations of combinatorial theory. VIII. Finite operator calculus.
J. Math. Anal. Appl. 42, pp. 684–760.
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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media.
In Differential Operators and Related Topics, Vol. I (Odessa,
1997),
Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
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7: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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Bounded and Unbounded Linear Operators
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… ►Spectrum of an Operator
…8: 25.17 Physical Applications
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►This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian.
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9: 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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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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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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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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10: 8 Incomplete Gamma and Related
Functions
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