matrix orthogonal polynomials
Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
... with some specific initial conditions we will see that the Weyl function of J and the complex measure of orthogonality, given by the general- ized Markov function, associated with the system of matrix ...
20
On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
... with orthogonal polynomials, generalized orthogonality, and Darboux transformations, see ...multiple orthogonal polynomials, and subsequently multi-component ...to orthogonal ...
9
Matrix orthogonal polynomials whose derivatives are also orthogonal
... related matrix parameters, such as the norm of the monic orthogonal polynomials, the coefficients of the three term recurrence relation or the coefficients of the linear relation between the ...
38
Matrix orthogonal laurent polynomials on the unit circle and toda type integrable systems
... identity matrix was found; see also ...this matrix situation and the appearance of non-Abelian discrete versions of Painlev´e I were explored , showing singularity confinement –see [32]; for Riemann–Hilbert ...
40
Average characteristic polynomials for multiple orthogonal polynomial ensembles
... Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal ...Riemann–Hilbert matrix Y consisting of four blocks Y 1 , 1 , Y 1 , 2 , Y 2 , 1 and Y 2 , 2 ...
35
Multivariate orthogonal polynomials and integrable systems
... multivariate orthogonal polynomials? To answer this question we consulted [39] and we readily noticed the ubiquity of the Gauss–Borel factorization in the subject, and therefore the opportunity to link it ...
74
Darboux Transforms and 2-Orthogonal Polynomials
... tridiagonal matrix J , as well as the transformation of Darboux and the Darboux transform without ...tridiagonal matrix a J 1 associated with the linear ...
5
On conjectures of Stenger in the theory of orthogonal polynomials
... Lagrange polynomials (n) k ) for degrees 2 ≤ n ≤ 40 and arbitrary α > –1, we need a routine that generates the respective recurrence coefficients for the orthogonal ...
27
On 2 orthogonal polynomials of Laguerre type
... for polynomials, defined and studied in a differ- ent context in [17], appears as a particular case of the general notion of biorthogonal- ity described in ...d-orthogonal polynomials is that they ...
20
A class of orthogonal polynomials of a new type
... Here we see that for different values of v we shall obtain m different differential equations, but solutions of these differential equations are orthogonal in the.. is obviously replaced[r] ...
10
Turán inequalities for symmetric orthogonal polynomials
... This method is shown to imply the positivity of Tur determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions... KEY WORDS AND PHRASES..[r] ...
7
Asymptotic Properties of Orthogonal and Extremal Polynomials
... study orthogonal polynomials (see for example [16, 49, 58, 65, 72, 73, 74]), especially in deriving root asymptotics and exploring the consequences of the notion of regularity (see ...
116
arxiv: v1 [math.pr] 26 Dec 2020
... In this section, we consider a generalization of the original Burnside process, which we will call “twisted Burnside process”. This will allow deformation of the examples above to give a natural process with a larger ...
25
Generating new classes of orthogonal polynomials
... Given a sequence of monic orthogonal polynomials MOPS, {Pn}, with respect to a quasi-definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn[r] ...
14
Identification of Microcalcifications with Orthogonal Polynomials Model
... Breast cancer is one of the leading causes of women mortality in the world. Mammography has been proved to be the primary radiologic procedure for the early detection of breast cancer. The two main indicators of breast ...
7
On Certain Wronskians of Multiple Orthogonal Polynomials
... gonal polynomials associated with a path connecting two ...for orthogonal polynomials due to Karlin and Szeg˝ ...characteristic polynomials for multiple orthogonal polynomial ensembles ...
19
Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials
... In this section, we will first fix some notations that will be used throughout this paper and then recall the necessary basic facts about orthogonal polynomials. As we will limit the facts to the minimum, the ...
15
Classical 2 orthogonal polynomials and differential equations
... Remark 3.2. We see that the determination of all the 2-orthogonal sequences goes through the resolution of the system (3.1)–(3.8). Many authors have tried to solve it, but up to now, its resolution is still giving ...
32
Zeros of random orthogonal polynomials on the unit circle
... In this chapter we will present a few basic results in the theory of orthogonal polynomials on the unit circle. Special attention will be devoted to the zeros of these polynomials and to the CMV ...
98
Spectral Theory for Generalized Bounded Variation Perturbations of Orthogonal Polynomials and Schrödinger Operators
... of orthogonal polynomials, orthogonality and the recurrence relation are cornerstones of the theory, so spectral theory focuses on the two cases when the measure is supported in R or ∂ D , which are (up to ...
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