Ole Fredrik Brevig

activity

20132026

most citedThe multiplicative Hilbert matrix

57 citations · 299 across the 47 of their papers we have counts for

collaborators

50 papers

math.FA2026

Extremals for linear functionals on $H^{p}$ are outer when $0 < p < 1$

Ole Fredrik Brevig, Øistein Søvik

Let $L$ be a nontrivial bounded linear functional on the Hardy space $H^{p}$ of the unit disc. We prove that if $0 < p < 1$ and if $f$ in the unit sphere of $H^{p}$ satisfies $L (f) = ∥ L ∥$ ,…

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.CA2026

Mean values, order, and convergence in the Hardy space of Dirichlet series

Ole Fredrik Brevig, Athanasios Kouroupis

Let $H^{2}$ denote the Hilbert space of Dirichlet series with square-summable coefficients. It follows from a theorem of Bohr that if $f$ in $H^{2}$ has a bounded a…

astro-ph.SR2026

Spectroscopic Study of the Circularly Polarised Radio Source TYC 2834-1385-1: An Active Binary

Tamara A. S. Bleeker, Alexander Hoogerbrug, Elise Koo +2

Close binaries with active chromospheres have recently been shown to emit circularly polarised radio emission at low frequencies, motivating detailed studies of their orbital prope…

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

A simple proof that the Riesz projection is bounded on $L^{p} (T)$ for $1 < p < \infty$

Ole Fredrik Brevig

Let $P$ denote the Riesz projection on the unit circle $T$ and suppose that $1 < p < \infty$ . We present a simple proof of the bound $\|\mathbf{P}f\|_p \leq \max(p,q)…

math.CA2026

Harald Bohr's splitting theorem

Viktor Andersson, Ole Fredrik Brevig, Athanasios Kouroupis

We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum…

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.CA2025

Carlson's theorem and vertical limit functions

Ole Fredrik Brevig, Athanasios Kouroupis

We extend a classical theorem of Carlson on moments of Dirichlet series from $p = 2$ to $1 \leq p < \infty$ . When combined with the ergodic theorem for the Kronecker flow, a coherent…

math.CV2024

Two footnotes to the F. & M. Riesz theorem

Ole Fredrik Brevig

We present a new proof of the F. & M. Riesz theorem on analytic measures of the unit circle $T$ that is based the following elementary inequality: If $f$ is analytic in th…

math.CA2024

Almost periodicity and boundary values of Dirichlet series

Ole Fredrik Brevig, Athanasios Kouroupis, Karl-Mikael Perfekt

We employ almost periodicity to establish analogues of the Hardy--Stein identity and the Littlewood--Paley formula for Hardy spaces of Dirichlet series. A construction of Saksman a…

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

Norm attaining vectors and Hilbert points

Konstantinos Bampouras, Ole Fredrik Brevig

Let $H$ be a Hilbert space that can be embedded as a dense subspace of a Banach space $X$ such that the norm of the embedding is equal to $1$ . We consider the following statements…

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.

math.CV2023★ 4 cited

An extension of Bohr's theorem

Ole Fredrik Brevig, Athanasios Kouroupis

The following extension of Bohr's theorem is established: If a somewhere convergent Dirichlet series $f$ has an analytic continuation to the half-plane $\mathbb{C}_θ= \{s = σ+it\,:…

math.CA2023★ 3 cited

The best constant in a Hilbert-type inequality

Ole Fredrik Brevig

We establish that \[\sum_{m=1}^\infty \sum_{n=1}^\infty a_m \overline{a_n} \frac{mn}{(\max(m,n))^3} \leq \frac{4}{3}\sum_{m=1}^\infty |a_m|^2\] holds for every square-summable sequ…

math.FA2023★ 1 cited

Maximal norm Hankel operators

Ole Fredrik Brevig, Kristian Seip

A Hankel operator $H_{φ}$ on the Hardy space $H^{2}$ of the unit circle with analytic symbol $φ$ has minimal norm if $∥ H_{φ} ∥ = ∥ φ ∥_{2}$ and maximal norm if $\|\mathbf{…

math.CA2022★ 5 cited

Point evaluation in Paley--Wiener spaces

Ole Fredrik Brevig, Andrés Chirre, Joaquim Ortega-Cerdà +1

We study the norm of point evaluation at the origin in the Paley--Wiener space $P W^{p}$ for $0 < p < \infty$ , i. e., we search for the smallest positive constant $C$ , called $\mathsc…

math.FA2022★ 2 cited

Correction to: Weak product spaces of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

We correct the proof of Theorem~8 in [\emph{Weak product spaces of Dirichlet series}, Integral Equations Operator Theory \textbf{86} (2016), no.~4, 453--473.]

math.FA2022★ 2 cited

The Nehari problem for the Paley--Wiener space of a disc

Ole Fredrik Brevig, Karl-Mikael Perfekt

There is a bounded Hankel operator on the Paley--Wiener space of a disc in $R^{2}$ which does not arise from a bounded symbol.

math.FA2022★ 2 cited

Hilbert points in Hilbert space-valued $L^{p}$ spaces

Ole Fredrik Brevig, Sigrid Grepstad

Let $H$ be a Hilbert space and $(Ω, F, μ)$ a probability space. A Hilbert point in $L^{p} (Ω; H)$ is a nontrivial function $φ$ such that $∥ φ ∥_{p} \leq ∥ φ + f ∥_{p}$ whenever $\la…

math.FA2021★ 2 cited

Orthogonal decomposition of composition operators on the $H^{2}$ space of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

Let $H^{2}$ denote the Hilbert space of Dirichlet series with square-summable coefficients. We study composition operators $C_{φ}$ on $H^{2}$ which are gene…

math.FA2021

Minimal norm Hankel operators

Ole Fredrik Brevig

Let $φ$ be a function in the Hardy space $H^{2} (T^{d})$ . The associated (small) Hankel operator $H_{φ}$ is said to have minimal norm if the general lower norm bound $\|…

math.FA2021★ 3 cited

Hilbert points in Hardy spaces

Ole Fredrik Brevig, Joaquim Ortega-Cerdà, Kristian Seip

A Hilbert point in $H^{p} (T^{d})$ , for $d \geq 1$ and $1 \leq p \leq \infty$ , is a nontrivial function $φ$ in $H^{p} (T^{d})$ such that $\| φ\|_{H^p(\mathbb{T}^d)} \leq \|φ+…

Extremals for linear functionals on Hp are outer when 0<p<1

Contractivity of Rudin's diagonal restriction operator for Hp of the polydisc

Mean values, order, and convergence in the Hardy space of Dirichlet series

Spectroscopic Study of the Circularly Polarised Radio Source TYC 2834-1385-1: An Active Binary

Bohr sets for multiplier algebras of complete Pick spaces

A simple proof that the Riesz projection is bounded on Lp(T) for 1<p<∞

Harald Bohr's splitting theorem

Contractive Hardy--Littlewood inequalities in the Dirichlet range

Carlson's theorem and vertical limit functions

Two footnotes to the F. & M. Riesz theorem

Almost periodicity and boundary values of Dirichlet series

Critical exponents of the Riesz projection

Norm attaining vectors and Hilbert points

The norm of the backward shift on H1 is 3​2​

An extension of Bohr's theorem

The best constant in a Hilbert-type inequality

Maximal norm Hankel operators

Point evaluation in Paley--Wiener spaces

Correction to: Weak product spaces of Dirichlet series

The Nehari problem for the Paley--Wiener space of a disc

Hilbert points in Hilbert space-valued Lp spaces

Orthogonal decomposition of composition operators on the H2 space of Dirichlet series

Minimal norm Hankel operators

Hilbert points in Hardy spaces

Extremals for linear functionals on $H^{p}$ are outer when $0 < p < 1$

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

A simple proof that the Riesz projection is bounded on $L^{p} (T)$ for $1 < p < \infty$

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

Hilbert points in Hilbert space-valued $L^{p}$ spaces

Orthogonal decomposition of composition operators on the $H^{2}$ space of Dirichlet series