A. Ranga

activity

20132022

most citedPara-orthogonal polynomials on the unit circle satisfying three term recurrence formulas

17 citations · 51 across the 11 of their papers we have counts for

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11 papers · 1 filter

math.CA2022

Complementary Romanovski-Routh polynomials and their zeros

Luana L. Silva Ribeiro, Alagacone Sri Ranga, Yen Chi Lun

The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomia…

math.CA2018

Quadrature rules from a $R_{I I}$ type recurrence relation and associated quadrature rules on the unit circle

Cleonice F. Bracciali, Junior A. Pereira, A. Sri Ranga

We consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special $R_{I I}$ recurrence relation. We also loo…

math.CA2018

Complementary Romanovski-Routh polynomials: From orthogonal polynomials on the unit circle to Coulomb wave functions

A. Martínez-Finkelshtein, L. L. Silva Ribeiro, A. Sri Ranga +1

We consider properties and applications of a sequence of polynomials known as complementary Romanovski-Routh polynomials (CRR polynomials for short). These polynomials, which follo…

math.CA2017★ 5 cited

Christoffel formula for kernel polynomials on the unit circle

Cleonice F. Bracciali, Andrei Martínez-Finkelshtein, A. Sri Ranga +1

Given a nontrivial positive measure $μ$ on the unit circle, the associated Christoffel-Darboux kernels are $K_{n} (z, w; μ) = \sum_{k = 0}^{n} φ_{k} (w; μ) φ_{k} (z; μ)$ , $n \geq…

math.CA2016

Extended relativistic Toda lattice, L-orthogonal polynomials and associated Lax pair

Cleonice F. Bracciali, Jairo S. Silva, A. Sri Ranga

When a measure $ψ (x)$ on the real line is subjected to the modification $d ψ^{(t)} (x) = e^{- t x} d ψ (x)$ , then the coefficients of the recurrence relation of the orthogonal polynomia…

math.CA2016★ 2 cited

Two families of orthogonal polynomials on the unit circle from basic hypergeometric functions

A. Sri Ranga

The sequence ${_{2} ϕ_{1} (q^{- k}, q^{b + 1}; q^{- b - k + 1}; q, q^{- b + 1/2} z)}_{k \geq 0}$ of basic hypergeometric polynomials is known to be orthogonal on the uni…

math.CA2016

Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences

Cleonice F. Bracciali, Jairo S. Silva, A. Sri Ranga +1

It was shown recently that associated with a pair of real sequences ${{c_{n}}_{n = 1}^{\infty}, {d_{n}}_{n = 1}^{\infty}}$ , with ${d_{n}}_{n = 1}^{\infty}$ a positive chain seque…

math.CA2016★ 1 cited

$R_{I I}$ type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle

Mourad E. H. Ismail, Alagacone Sri Ranga

We consider a sequence of polynomials ${P_{n}}_{n \geq 0}$ satisfying a special $R_{I I}$ type recurrence relation where the zeros of $P_{n}$ are simple and lie on the real line. It t…

math.CA2016★ 4 cited

Orthogonal Polynomials Associated with Complementary Chain Sequences

Kiran Kumar Behera, A. Sriranga, A. Swaminathan

Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using…

math.CA2015★ 9 cited

Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure

A. Martinez-Finkelshtein, A. Sri Ranga, Daniel O. Veronese

Given a non-trivial Borel measure $μ$ on the unit circle $T$ , the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at $z = 1$ consti…

math.CA2014★ 17 cited

Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas

Cleonice F. Bracciali, Alagacone Sri Ranga, Anbhu Swaminathan

When a nontrivial measure $μ$ on the unit circle satisfies the symmetry $d μ (e^{i (2 π - θ)}) = - d μ (e^{i θ})$ then the associated OPUC, say $S_{n}$ , are all real. In this case, Delsarte a…