Stefan Kahler

activity

20182026

most citedTurán's inequality, nonnegative linearization and amenability properties for associated symmetric Pollaczek polynomials

2 citations · 3 across the 7 of their papers we have counts for

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5 papers · 1 filter

math.CA2026

On Turán's inequality: new general criteria, nonnegative representations and the class of generalized Chebyshev polynomials

Stefan Kahler

Originally, Turán's inequality states that if $(P_{n} (x))_{n \in N_{0}}$ is the sequence of Legendre polynomials, then $Δ_{n} (x) := P_{n}^{2} (x) - P_{n + 1} (x) P_{n - 1} (x) \geq 0$ for all $n\in…

math.CA2026

A new class of orthogonal polynomials

Stefan Kahler, Josef Obermaier

We consider random walk polynomial sequences $(P_{n} (x))_{n \in N_{0}} \subseteq R [x]$ given by recurrence relations of the form $P_{0} (x) = 1$ , $P_{1} (x) = x$ and $x P_n(x)=a_n…

math.CA2023

Expansions and Characterizations of Sieved Random Walk Polynomials

Stefan Kahler

We consider random walk polynomial sequences $(P_{n} (x))_{n \in N_{0}} \subseteq R [x]$ given by recurrence relations $P_{0} (x) = 1$ , $P_{1} (x) = x$ , $x P_n(x)=(1-c_n)P_{n+1}(x)+c…

math.CA2022

Dual spaces vs. Haar measures of polynomial hypergroups

Stefan Kahler, Ryszard Szwarc

Many symmetric orthogonal polynomials $(P_{n} (x))_{n \in N_{0}}$ induce a hypergroup structure on $N_{0}$ . The Haar measure is the counting measure weighted with $h(n):=1…

math.CA2018

Nonnegative and strictly positive linearization of Jacobi and generalized Chebyshev polynomials

Stefan Kahler

In the theory of orthogonal polynomials, as well as in its intersection with harmonic analysis, it is an important problem to decide whether a given orthogonal polynomial sequence…