Frantivsek vStampach

activity

20242026

collaborators

8 papers

math.CA2026

Optimal discrete $p$ -Hardy-Rellich-Birman inequalities

FrantiÅ¡ek Å tampach, Jakub Waclawek

We present a theory for constructing optimal lower bounds for the discrete half-line $p$ -Laplacian of higher order $ℓ \in N$ and general $p > 1$ . The abstract framework int…

math.CA2026

The $p$ -Hardy-Rellich-Birman inequalities on the half-line

FrantiÅ¡ek Å tampach, Jakub Waclawek

The classical discrete $p$ -Hardy inequality establishes a sharp relationship between the $ℓ^{p}$ -norms of a sequence and its discrete derivative. In this paper, we generalize th…

math.SP2026

SchrÃ¶dinger operators on the half-line with integrable complex potentials

Alexander Pushnitski, FrantiÅ¡ek Å tampach

In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line SchrÃ¶dinger operator with a \emph{complex} bounded potential $q$ , serving as a substitute…

math.CA2025

Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients

Rostyslav Kozhan, FrantiÅ¡ek Å tampach

We study asymptotic behavior of orthogonal polynomials on the unit circle with varying Verblunsky coefficients $I^\pm_{n, N}$ when the ratio $n / N$ converges as $n, N \to \infty$ . First, w…

math.SP2025

The Borg-Marchenko uniqueness theorem for complex potentials

Alexander Pushnitski, FrantiÅ¡ek Å tampach

We introduce and study a new theoretical concept of \textit{spectral pair} for a SchrÃ¶dinger operator $H$ in $L^{2} (R_{+})$ with a bounded \textit{complex-valued} potential…

math.CA2025

A Herglotz-Nevanlinna function from the optimal discrete $p$ -Hardy weight

FrantiÅ¡ek Å tampach, Jakub Waclawek

It was recently proved by Fischer, Keller, and Pogorzelski in [Integr. Equ. Oper. Theory, 95(24), 2023] that the classical discrete $p$ -Hardy inequality admits an improvement, and…

Optimal discrete p-Hardy-Rellich-Birman inequalities

The p-Hardy-Rellich-Birman inequalities on the half-line

SchrÃ¶dinger operators on the half-line with integrable complex potentials

Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients

The Borg-Marchenko uniqueness theorem for complex potentials

A Herglotz-Nevanlinna function from the optimal discrete p-Hardy weight

Optimal discrete $p$ -Hardy-Rellich-Birman inequalities

The $p$ -Hardy-Rellich-Birman inequalities on the half-line

A Herglotz-Nevanlinna function from the optimal discrete $p$ -Hardy weight