Kristian Seip

activity

20232026

collaborators

8 papers

math.CA2026

The zeros of point evaluation extremals in Paley-Wiener spaces

Andriy Bondarenko, Joaquim Ortega-Cerdà, Kristian Seip

For $1 \leq p < \infty$ , $φ_{p}$ is the function of minimal $L^{p}$ norm among all functions $f$ of exponential type at most $π$ for which $f (0) = 1$ . We start from the ansatz that the pos…

math.FA2026

Contractivity of Rudin's diagonal restriction operator for $H^{p}$ of the polydisc

Ole Fredrik Brevig, Javier Gómez-Serrano, Joaquim Ortega-Cerdà +1

We establish that Rudin's diagonal restriction operator is contractive from the Hardy space $H^{p}$ of the bidisc to the Bergman space $A^{p}$ of the disc for $2 \leq p < \infty$ , and cha…

math.FA2026

Bohr sets for multiplier algebras of complete Pick spaces

Ole Fredrik Brevig, Kristian Seip, Ilya Zlotnikov

We reexamine F. Wiener's classical proof that the Bohr radius of $H^{\infty}$ is $1/3$ . We replace $H^{\infty}$ by the multiplier algebras of complete Pick spaces and describe the Bohr…

math.CA2026

Fourier-invariant functions with dense zero sets

Andriy Bondarenko, Kristian Seip

For every $0 \leq β \leq 1/2$ , we construct a nonzero real-valued continuous function $f_{β}$ in $L^{1} (R) \cap L^{2} (R)$ such that $f_{β} = f_{β}$ and $f_β(\sqrt{n}/[\lo…

math.NT2025

The basis functions of Fourier interpolation

David Berghaus, Andriy Bondarenko, Danylo Radchenko +2

The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire…

math.CV2025

Contractive Hardy--Littlewood inequalities in the Dirichlet range

Ole Fredrik Brevig, Aleksei Kulikov, Kristian Seip +1

The class $A_{α}^{p}$ consists of those analytic functions $f$ in the unit disc such that \[\|f\|_{α,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{α-1} \,dr <…

math.FA2024

Critical exponents of the Riesz projection

Ole Fredrik Brevig, Adrián Llinares, Kristian Seip

Let $p_{d} (q)$ denote the critical exponent of the Riesz projection from $L^{q} (T^{d})$ to the Hardy space $H^{p} (T^{d})$ , where $T$ is the unit circle.…

math.FA2023

The norm of the backward shift on $H^{1}$ is $\frac{2}{3}$

Ole Fredrik Brevig, Kristian Seip

We show that the norm of the backward shift operator on $H^{1}$ is $2/ 3$ , and we identify the functions for which the norm is attained.