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Autor Gómez-Ullate Otaiza, David |
Documentos disponibles escritos por este autor (30)
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Finkel Morgenstern, Federico ; Gómez-Ullate Otaiza, David ; González López, Artemio ; Rodríguez González, Miguel Ángel ; Zhdanov, R. | Springer | 2003-02The B-N hyperbolic Sutherland spin model is expressed in terms of a suitable set of commuting Dunkl operators. This fact is exploited to derive a complete family of commuting integrals of motion of the model, thus establishing its integrability.[...]![]()
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The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schrodinger's equation to have constant sign in its domain of definition. We extend this result by giving explicit formulas[...]![]()
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We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvab[...]![]()
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Our goal in this paper is to extend the theory of quasi-exactly solvable Schrodinger operators beyond the Lie-algebraic class. Let P-n be the space of nth degree polynomials in one variable. We first analyze exceptional polynomial subspaces M su[...]![]()
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We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmo[...]![]()
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Gómez-Ullate Otaiza, David ; Kasman, Alex ; Kuijlaars, Arno B. J. ; Milson, Robert | Academic Press-Elsevier Science | 2016-04The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctio[...]![]()
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In this paper we perform a statistical analysis of the high-frequency returns of the IBEX35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in many di[...]![]()
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Gómez-Ullate Otaiza, David ; Kamran, Niky ; Milson, Robert | American Institute of Mathematical Sciences | 2007-05In this paper we derive structure theorems which characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful conc[...]![]()
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Gómez-Ullate Otaiza, David ; Lafortune, S. ; Winternitz, P. | American Institute of Physics | 1999-06The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to ten dimensional. The equatio[...]![]()
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We investigate the backward Darboux transformations (addition of the lowest bound state) of shape-invariant potentials on the line, and classify the subclass of algebraic deformations, those for which the potential and the bound states are simpl[...]![]()
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Calogero, F. ; Gómez-Ullate Otaiza, David ; Santin, Paolo M. ; Sommacal, M | IOP Publishing | 2005-10-14We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a three-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riem[...]![]()
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Calogero, F. ; Gómez-Ullate Otaiza, David ; Santini, P. M. ; Sommacal, M. | IOP publishing ltd | 2009-01-09We investigate the dynamics defined by the following set of three coupled first-order ODEs: (z) over dot (n) + i omega z(n) = g(n+2)/z(n) - z(n+1) + g(n+1)/z(n) - z(n+2) It is shown that the system can be reduced to quadratures which can be expr[...]![]()
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Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial dat[...]![]()
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It has been recently discovered that exceptional families of Sturm-Liouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of excepti[...]![]()
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We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits c[...]