Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 25 Aug 2019 04:51:24 GMT2019-08-25T04:51:24Z50141Coherent pairs of linear functionals on the unit circlehttp://hdl.handle.net/10316/4581Title: Coherent pairs of linear functionals on the unit circle
Authors: Branquinho, A.; Moreno, A. Foulquié; Marcellán, F.; Rebocho, M. N.
Abstract: In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ([mu]0,[mu]1) is a coherent pair of measures on the unit circle, then [mu]0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with [mu]1 is a specific rational transformation of the linear functional corresponding to [mu]0. Some examples are given.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45812008-01-01T00:00:00ZMatrix interpretation of multiple orthogonalityhttp://hdl.handle.net/10316/11204Title: Matrix interpretation of multiple orthogonality
Authors: Branquinho, A.; Cotrim, L.; Moreno, A. Foulquié
Abstract: In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence
relation in terms of type II multiple orthogonal polynomials. We rewrite this
recurrence relation in matrix form and we obtain a three-term recurrence relation
for vector polynomials with matrix coefficients. We present a matrix interpretation
of the type II multi-ortogonality conditions. We state a Favard type theorem and
the expression for the resolvent function associated to the vector of linear functionals.
Finally a reinterpretation of the type II Hermite-Pad´e approximation in matrix
form is given.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112042008-01-01T00:00:00ZDynamics and interpretation of some integrable systems via multiple orthogonal polynomialshttp://hdl.handle.net/10316/11210Title: Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials
Authors: Barrios Rolanía, D.; Branquinho, A.; Moreno, A. Foulquié
Abstract: High-order non symmetric difference operators with complex coefficients
are considered. The correspondence between dynamics of the coefficients of
the operator defined by a Lax pair and its resolvent function is established. The
method of investigation is based on the analysis of the moments for the operator.
The solution of a discrete dynamical system is studied. We give explicit expressions
for the resolvent function and, under some conditions, the representation of the
vector of functionals, associated with the solution for the integrable systems.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112102008-01-01T00:00:00ZMatrix Sylvester equations in the theory of orthogonal polynomials on the unit circlehttp://hdl.handle.net/10316/11261Title: Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle
Authors: Branquinho, A.; Rebocho, M. N.
Abstract: In this paper we characterize sequences of polynomials on the unit
circle, orthogonal with respect to a Hermitian linear functional such that its corresponding
Carath´eodory function satisfies a Riccati differential equation with polynomial
coefficients, in terms of matrix Sylvester differential equations. Furthermore,
under certain conditions, we give a representation of such sequences in terms of
semi-classical orthogonal polynomials on the unit circle. For the particular case of
semi-classical orthogonal polynomials on the unit circle, a characterization in terms
of first order differential systems is established.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112612008-01-01T00:00:00ZOn differential equations for orthogonal polynomials on the unit circlehttp://hdl.handle.net/10316/11242Title: On differential equations for orthogonal polynomials on the unit circle
Authors: Branquinho, A.; Rebocho, M. N.
Abstract: In this paper we characterize sequences of orthogonal polynomials on
the unit circle whose corresponding Carath´eodory function satisfies a Riccati differential
equation with polynomial coefficients, in terms of second order matrix
differential equations.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112422008-01-01T00:00:00ZOn the relation between the full Kostant-Toda lattice and multiple orthogonal polynomialshttp://hdl.handle.net/10316/13635Title: On the relation between the full Kostant-Toda lattice and multiple orthogonal polynomials
Authors: Barros Rolanía, D.; Branquinho, A.; Foulquié Moreno, A.
Abstract: The correspondence between a high-order non symmetric difference
operator with complex coefficients and the evolution of an operator defined by a
Lax pair is established. The solution of the discrete dynamical system is studied,
giving explicit expressions for the resolvent function and, under some conditions,
the representation of the vector of functionals, associated with the solution for our
integrable systems. The method of investigation is based on the evolutions of the
matrical moments.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136352009-01-01T00:00:00ZComplex high order Toda and Volterra latticeshttp://hdl.handle.net/10316/11269Title: Complex high order Toda and Volterra lattices
Authors: Barrios Rolanía, D.; Branquinho, A.
Abstract: Given a solution of a high order Toda lattice we construct a one parameter
family of new solutions. In our method, we use a set of B¨acklund transformations
in such a way that each new generalized Toda solution is related to a
generalized Volterra solution.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112692008-01-01T00:00:00ZDistributional equation for Laguerre-Hahn functionals on the unit circlehttp://hdl.handle.net/10316/11283Title: Distributional equation for Laguerre-Hahn functionals on the unit circle
Authors: Branquinho, A.; Rebocho, M. N.
Abstract: Let u be a hermitian linear functional defined in the linear space of
Laurent polynomials and F its corresponding Carath´eodory function. We establish
the equivalence between a Riccati differential equation with polynomial coefficients
for F, zAF′ = BF2+CF +D and a distributional equation for u, D(Au) = B1u2+
C1u+H1L, where L is the Lebesgue functional, and the polynomials B1,C1,D1 are
defined in terms of the polynomials A,B,C,D
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/112832007-01-01T00:00:00ZRiemann-Hilbert problem associated with Angelesco systemshttp://hdl.handle.net/10316/11290Title: Riemann-Hilbert problem associated with Angelesco systems
Authors: Branquinho, A.; Fidalgo Prieto, U.; Moreno, A. Foulquié
Abstract: Angelesco systems of measures with Jacobi type weights are considered.
For such systems, strong asymptotic development expressions for sequences
of associated Hermite-Pad´e approximants are found. In the procedure, an approach
from Riemann-Hilbert Problem plays a fundamental role.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/112902007-01-01T00:00:00ZRelative asymptotics for orthogonal matrix polynomialshttp://hdl.handle.net/10316/13707Title: Relative asymptotics for orthogonal matrix polynomials
Authors: Branquinho, A.; Marcellán, F.; Mendes, A.
Abstract: In this paper we study sequences of matrix polynomials that satisfy a
non-symmetric recurrence relation. To study this kind of sequences we use a vector
interpretation of the matrix orthogonality. In the context of these sequences of
matrix polynomials we introduce the concept of the generalized matrix Nevai class
and we give the ratio asymptotics between two consecutive polynomials belonging to
this class. We study the generalized matrix Chebyshev polynomials and we deduce
its explicit expression as well as we show some illustrative examples. The concept of
a Dirac delta functional is introduced. We show how the vector model that includes
a Dirac delta functional is a representation of a discrete Sobolev inner product. It
also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally,
the relative asymptotics between a polynomial in the generalized matrix Nevai class
and a polynomial that is orthogonal to a modification of the corresponding matrix
measure by the addition of a Dirac delta functional is deduced.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137072010-01-01T00:00:00ZOn the semiclassical character of orthogonal polynomials satisfying structure relationshttp://hdl.handle.net/10316/13712Title: On the semiclassical character of orthogonal polynomials satisfying structure relations
Authors: Branquinho, A.; Rebocho, M. N.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137122010-01-01T00:00:00ZVector interpretation of the matrix orthogonality on the real linehttp://hdl.handle.net/10316/13638Title: Vector interpretation of the matrix orthogonality on the real line
Authors: Branquinho, A.; Marcellán, F.; Mendes, A.
Abstract: In this paper we study sequences of vector orthogonal polynomials. The
vector orthogonality presented here provides a reinterpretation of what is known in
the literature as matrix orthogonality. These systems of orthogonal polynomials
satisfy three-term recurrence relations with matrix coefficients that do not obey
to any type of symmetry. In this sense the vectorial reinterpretation allows us to
study a non-symmetric case of the matrix orthogonality. We also prove that our
systems of polynomials are indeed orthonormal with respect to a complex measure
of orthogonality. Approximation problems of Hermite-Pad´e type are also discussed.
Finally, a Markov’s type theorem is presented.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136382009-01-01T00:00:00ZCharacterizations of Laguerre-Hahn affine orthogonal polynomials on the unit circlehttp://hdl.handle.net/10316/11309Title: Characterizations of Laguerre-Hahn affine orthogonal polynomials on the unit circle
Authors: Branquinho, A.; Rebocho, M. N.
Abstract: In this work we characterize a monic polynomial sequence, orthogonal
with respect to a hermitian linear functional u that satisfies a functional equation
D(Au) = Bu + zHL, where A,B and H are polynomials and L is the Lebesgue
functional, in terms of a first order linear differential equation for the Carath´eodory
function associated with u and in terms of a first order structure relation for the
orthogonal polynomials.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113092007-01-01T00:00:00ZAlgebraic theory of multiple orthogonal polynomialshttp://hdl.handle.net/10316/11180Title: Algebraic theory of multiple orthogonal polynomials
Authors: Branquinho, A.; Cotrim, L.; Moreno, A. Foulquié
Abstract: In this work we present an algebraic theory of multiple orthogonal
polynomials. Our departure point is the three term recurrence relation, with matrix
coefficients, satisfied by a sequence of vector multiple orthogonal polynomials. We
give some characterizations of multiple orthogonal polynomials including recurrence
relations, a Favard type theorem and a Christoffel-Darboux type formulas. An
reinterpretation of the problems of Hermite-Pad´e approximation is presented.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111802009-01-01T00:00:00Z