Cardoso, J. L.
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Cardoso
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J. L.
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8B17-66EA-A14A
35386045600
M-9078-2018Projetos de investigação
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18 resultados
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Publicação Acesso Restrito Publicação Acesso Restrito Variations around a general quantum operator2021-04-17 - Cardoso, J. L.Let I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s_0 ∈ I that satisfies (s0 − t)(β(t) − t) ≥ 0 for all t ∈ I, where the equality holds only when t = s_0. For appropriate choices of the function β, the quantum operator defined by Hamza et al., D_β[ f ](t) :=(f β(t) − f (t))/(β(t) − t) if t = s0 and Dβ[ f ](s0) := f '(s0) if t = s0, generalizes both the Jackson q-operator D_q and the Hahn (quantum derivative) operator, D_{q,ω}.With respect to the inverse of this general quantum difference operator, the β-integral, we study properties of the corresponding Lebesgue spaces L_β^p ([a, b]).Publicação Acesso Aberto The roots of the Third Jackson q-Bessel Function2003 - Abreu, L. D.; Bustoz, J.; Cardoso, J. L.We derive analytic bounds for the zeros of the third Jackson q-Bessel function J_ν^(3)(z;q).Publicação Acesso Restrito On the properties of special functions on the linear-type lattices2013 - Álvarez-Nodarse, R.; Cardoso, J. L.We present a general theory for studying the difference analogs of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference–recurrence relations for such functions. Finally, applications to q-classical polynomials are given.Publicação Acesso Restrito Basic Fourier Series: convergence on and outside the q-Linear Grid2011-02 - Cardoso, J. L.A q-type Hölder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S_q[f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding other conditions, one guarantees the (uniform) convergence of S_q[f] to f on and “outside” the set points of the q-linear grid.Publicação Acesso Restrito Variations around a general quantum operator2021-04 - Cardoso, J. L.Let I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s0 ∈ I that satisfies (s0 − t)(β(t) − t) ≥ 0 for all t ∈ I , where the equality holds only when t = s0. For appropriate choices of the function β, the quantum operator defined by Hamza et al., Dβ[ f ](t) := f β(t) − f (t) β(t) − t if t = s0 and Dβ[ f ](s0) := f (s0) if t = s0, generalizes both the Jackson q-operator Dq and the Hahn (quantum derivative) operator, Dq,ω.With respect to the inverse of this general quantum difference operator, the β-integral, we study properties of the corresponding Lebesgue spaces L p β ([a, b]).Publicação Acesso Restrito On recurrence relations for radial wave functions for the n-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study2006 - Álvarez-Nodarse, R.; Quintero, N. R.; Cardoso, J. L.Using a general procedure for finding recurrence relations for hypergeometric functions and polynomials introduced by Cardoso et al. [J. Phys. A, 36 (2003), pp. 2055-2068] we obtain some new recurrence relations for the radial wave functions of the N-th dimensional isotropic harmonic oscillators as well as the hydrogenlike atoms. A numerical analysis of such recurrences is also presented.Publicação Acesso Aberto Ladder type operators and recurrence relations for the radial wave functions of the N-th dimensional oscillators and hydrogenlike atoms2006 - Costa, E. M.; Cardoso, J. L.Using the method described in [11], we present some new ladder type operators and recurrence relations for the radial wave functions of the N-th dimensional isotropic harmonic oscillators and the hydrogenlike atoms.Publicação Acesso Restrito Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method2009 - Fernandes, C. M.; Álvarez-Nodarse, R.; Cardoso, J. L.The functions of hypergeometric-type are the solutions y=y_v(z) of the differential equation a(z)y′′ + b(z)y′ + c y = 0, where a(z) and b(z) are polynomials of degrees not higher than 2 and 1, respectively, and c is a constant. Here we consider a class of functions of hypergeometric type: those that satisfy the condition c+vb′ + 1/2v(v −1)a′′ = 0, where v is an arbitrary complex (fixed) number. We also assume that the coefficients of the polynomials a and b do not depend on v. To this class of functions belong Gauss, Kummer, and Hermite functions, and also the classical orthogonal polynomials. In this work, using the constructive approach introduced by Nikiforov and Uvarov, several structural properties of the hypergeometric-type functions y = y_v(z) are obtained. Applications to hypergeometric functions and classical orthogonal polynomials are also given.Publicação Acesso Restrito A β-Sturm–Liouville problem associated with the general quantum operator2021-05-20 - Cardoso, J. L.Let I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s0 ∈ I that satisfies (s0 −t)(β(t) − t) ≥ 0 for all t ∈ I, where the equality holds only when t =s0. The general quantum operator defined by Hamza et al.,Dβ[f ](t) := fβ(t)−f (t) β(t)−t if t = s0 and Dβ [f ](s0) := f (s0) if t = s0, generalizes the Jackson q-operator Dq and also the Hahn (quantum derivative) operator, Dq,ω. Regarding a β-Sturm–Liouville eigenvalue problem associated with the above operator Dβ , we construct the β-Lagrange’s identity, show that it is self-adjoint in L2 β ([a, b]), and exhibit some properties for the corresponding eigenvalues and eigenfunctions.