### Browsing by Author "Kalnins, E.G."

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Item Complete sets of invariants for dynamical systems that admit a separation of variables(2002-02) Kalnins, E.G.; Kress, J.M.; Pogosyan, G.; Miller, Jr., W.Show more Item Completeness of multiseparable superintegrability on the complex 2-sphere(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Completeness of mutiseparable superintegrability in E2, C(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Completeness of superintegrability in two dimensional constant curvature spaces(2000-12) Kalnins, E.G.; Kress, J.M.; Pogosyan, G.; Miller, Jr., W.Show more We classify the Hamiltonians H=px2+ py2 +V(x,y) of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H=J12+J22+ J32+V(x,y,z) on the complex 2-sphere where x2+y2+z2=1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.Show more Item Conformal Symmetries and Generalized Recurrences for Heat and Schrodinger Equations in One Spatial Dimension(1989) Kalnins, E.G.; Levine, Raphael D.; Miller, Jr., WillardShow more Item Contractions of Lie algebras: Applications to special functions and separation of variables(1999-06) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Coulomb-oscillator duality in spaces of constant curvature(1998-12) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Coulomb-oscillator duality in spaces of constant curvature(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item The Coulomb-oscillator relation on the N-sphere(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Exact and quasi-exact solvability of second order superintegrable quantum systems. II. Relation to separation of variables(2006-12) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Show more Item Families of Orthogonal and Biorthogonal Polynomials on the N-Sphere(1989) Kalnins, E.G.; Miller, Jr., Willard; Tratnik, M.V.Show more Item Hypergeometric expansions of Heun polynomials(1990-07) Kalnins, E.G.; Miller, Jr., WillardShow more Item Intrinsic characterisation of the separation constant for spin one and gravitational perturbations in Kerr geometry(1994-04) Kalnins, E.G.; Williams, G.C.; Miller, Jr., WillardShow more Item Models for the 3D singular isotropic oscillator quadratic algebra(2008-11-06) Kalnins, E.G.; Miller Jr., W.; Post, SarahShow more We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in $n$ dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.Show more Item Models of q-algebra representations I. Tensor products of special unitary and oscillator algebras(1991-08) Kalnins, E.G.; Manocha, H.L.; Miller, Jr., WillardShow more Item Models of q-algebra representations: Matrix elements of the q-oscillator algebra(1992-09) Kalnins, E.G.; Miller, Jr., Willard; Mukherjee, SanchitaShow more Item Models of q-algebra representations: Matrix Elements of Uq(su2)(1992-08) Kalnins, E.G.; Miller, Jr., Willard; Mukherjee, SanchitaShow more Item Models of q-algebra representations: q-integral transforms and "addition theorems"(1993-07) Kalnins, E.G.; Miller, Jr., WillardShow more Item Models of q-algebra representations: the group of plane motions(1991-12) Kalnins, E.G.; Miller, Jr., Willard; Mukherjee, SanchitaShow more Item Models of quadratic quantum algebras and their relation to classical superintegrable systems(2008-09-12) Kalnins, E.G.; Miller Jr., W.; Post, SarahShow more We show how to construct realizations (models) of quadratic algebras for 2 dimensional second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.Show more