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We present two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with a polynomial of degree one. We denote these polynomials as X(1)-Ja[...]texto impreso
Gómez-Ullate Otaiza, David ; Kamran, Niky ; Milson, Robert | Academic Press-Elsevier Science | 2010-05We prove an extension of Bochner's classical result that characterizes the classical polynomial families as eigenfunctions of a second-order differential operator with polynomial coefficients. The extended result involves considering differentia[...]texto impreso
Gallego, Víctor ; Suarez García, Pablo ; Angulo, Pablo ; Gómez-Ullate Otaiza, David | Wiley | 2019-05We propose a robust implementation of the Nerlove-Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a countrywide fast-food franchise network with its weekly sales. Due to t[...]texto impreso
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotic ally to functions periodic with the sa [...]texto impreso
Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm-Liouville problems, but without the assumption that an eigenpolynomial of every degree is present. In this sense, they generalize the classical families of Hermi[...]texto impreso
This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time tau. In this work we consi[...]texto impreso
Gómez-Ullate Otaiza, David ; González López, Artemio ; Rodríguez González, Miguel Ángel | Elsevier Science BV | 2001-05-28A quantum Hamiltonian describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is introduced. For a discrete set of values of the strength of the external potential, it is show[...]texto impreso
We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described X(m) Laguerre polynomials in terms of an isospectral Darboux transformation. We al[...]texto impreso
Gómez-Ullate Otaiza, David ; Grandati, Yves ; Milson, Robert | American Institute of Physics | 2014-04Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-Backlund transformations. It allows us to establish novel bi-l[...]texto impreso
Duque Rodriguez, Juan ; Gómez-Ullate Otaiza, David ; Mejia-Monasterio, Carlos | American Physical Society | 2014-04-24In olfactory search an immobile target emits chemical molecules at constant rate. The molecules are transported by the medium, which is assumed to be turbulent. Considering a searcher able to detect such chemical signals and whose motion follows[...]texto impreso
Finkel Morgenstern, Federico ; Gómez-Ullate Otaiza, David ; González López, Artemio ; Rodríguez González, Miguel Ángel | Springer | 2001-08A new family of AN-type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactl[...]texto impreso
Gómez-Ullate Otaiza, David ; González López, Artemio ; Rodríguez González, Miguel Ángel | IOP Publishing | 2000-10-20We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly solvable models include rational and hyperbolic potentials related to root s[...]texto impreso
In this paper we discuss a family of toy models for many-body interactions including velocity-dependent forces. By generalizing a construction due to Calogero, we obtain a class of N-body problems in the plane which have periodic orbits for a la[...]texto impreso
Finkel Morgenstern, Federico ; Gómez-Ullate Otaiza, David ; González López, Artemio ; Rodríguez González, Miguel Ángel | Elsevier | 2001-10-15We construct several new families of exactly and quasi-exactly solvable BCN-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of a new family of Dunkl operators of B-N type which, togethe[...]texto impreso
We survey some recent developments in the theory of orthogonal polynomials defined by differential equations. The key finding is that there exist orthogonal polynomials defined by 2nd order differential equations that fall outside the classical [...]
