Karl-Mikael Perfekt

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20112026

most citedThe multiplicative Hilbert matrix

57 citations · 347 across the 45 of their papers we have counts for

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31 papers · 1 filter

math.FA2026

A Fejér--Riesz inequality for Dirichlet series

Karl-Mikael Perfekt

We prove the following inequality for Dirichlet polynomials: \[ \int_0^1 |f(1/2+σ)|\,dσ\lesssim \lim_{T\to\infty} \frac{1}{2T} \int_{-T}^T |f(it)| \, dt. \] In particular, for a Di…

math.FA2026

Recovering Product BMO from Schatten Hankel operators

Konstantinos Bampouras, Karl-Mikael Perfekt

We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^{p}$ , $p < \infty$ , then it has a symbol in product BMO. In other words, the con…

math.FA2024

Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions

Konstantinos Bampouras, Karl-Mikael Perfekt

We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $Ω \subset R^{n}$ , both for bounded and unbounded domains. In particular, the clas…

math.FA2023

Cyclicity and iterated logarithms in the Drury-Arveson space

Alexandru Aleman, Karl-Mikael Perfekt, Stefan Richter +2

Let $H_{d}^{2}$ be the Drury-Arveson space, and let $f \in H_{d}^{2}$ have bounded argument and no zeros in $B_{d}$ . We show that $f$ is cyclic in $H_{d}^{2}$ if and only if $lo g f$ bel…

math.FA2023

Cyclicity in the Drury-Arveson space and other weighted Besov spaces

Alexandru Aleman, Karl-Mikael Perfekt, Stefan Richter +2

Let $H$ be a space of analytic functions on the unit ball $B_{d}$ in $C^{d}$ with multiplier algebra $Mult (H)$ . A function $f\in \mathcal{H…

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★ 8 cited

Composition operators on weighted Hilbert spaces of Dirichlet series

Athanasios Kouroupis, Karl-Mikael Perfekt

We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functi…

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.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★ 6 cited

The quasi-static plasmonic problem for polyhedra

Marta de León-Contreras, Karl-Mikael Perfekt

We characterize the essential spectrum of the plasmonic problem for polyhedra in $R^{3}$ . The description is particularly simple for convex polyhedra and permittivities $ε<…

math.FA2020★ 1 cited

Infinitely many embedded eigenvalues for the Neumann-Poincaré operator in 3D

Wei Li, Karl-Mikael Perfekt, Stephen P. Shipman

This article constructs a surface whose Neumann-Poincaré (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The surface is a sphere perturbe…

math.FA2020★ 17 cited

A mean counting function for Dirichlet series and compact composition operators

Ole Fredrik Brevig, Karl-Mikael Perfekt

We introduce a mean counting function for Dirichlet series, which plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function…

math.FA2020★ 4 cited

The spectrum of some Hardy kernel matrices

Ole Fredrik Brevig, Karl-Mikael Perfekt, Alexander Pushnitski

For $α > 0$ we consider the operator $K_{α} : ℓ^{2} \to ℓ^{2}$ corresponding to the matrix \[\left(\frac{(nm)^{-\frac{1}{2}+α}}{[\max(n,m)]^{2α}}\right)_{n,m=1}^\infty.\] By int…

math.FA2019

Atomic decompositions, two stars theorems, and distances for the Bourgain-Brezis-Mironescu space and other big spaces

Luigi D'Onofrio, Luigi Greco, Karl-Mikael Perfekt +2

Given a Banach space $E$ with a supremum-type norm induced by a collection of operators, we prove that $E$ is a dual space and provide an atomic decomposition of its predual. We ap…

math.FA2019★ 10 cited

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

Ole Fredrik Brevig, Karl-Mikael Perfekt

We consider composition operators $C_{φ}$ on the Hardy space of Dirichlet series $H^{2}$ , generated by Dirichlet series symbols $φ$ . We prove two different subordin…

math.FA2017★ 1 cited

On the spaces of bounded and compact multiplicative Hankel operators

Karl-Mikael Perfekt

A multiplicative Hankel operator is an operator with matrix representation $M (α) = {α (nm)}_{n, m = 1}^{\infty}$ , where $α$ is the generating sequence of $M (α)$ . Let $M$ and…

math.FA2017

Nehari's theorem for convex domain Hankel and Toeplitz operators in several variables

Marcus Carlsson, Karl-Mikael Perfekt

We prove Nehari's theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness cr…

math.FA2017

On the spectrum of the multiplicative Hilbert matrix

Karl-Mikael Perfekt, Alexander Pushnitski

We study the multiplicative Hilbert matrix, i.e. the infinite matrix with entries $(mn lo g (mn))^{- 1}$ for $m, n \geq 2$ . This matrix was recently introduced within the context…

math.FA2017★ 14 cited

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Frédéric Bayart, Ole Fredrik Brevig, Antti Haimi +2

We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's i…

math.FA2016★ 13 cited

On Helson matrices: moment problems, non-negativity, boundedness, and finite rank

Karl-Mikael Perfekt, Alexander Pushnitski

We study Helson matrices (also known as multiplicative Hankel matrices), i.e. infinite matrices of the form $M (α) = {α (nm)}_{n, m = 1}^{\infty}$ , where $α$ is a sequence of complex nu…

math.FA2016★ 54 cited

The essential spectrum of the Neumann--Poincare operator on a domain with corners

Karl-Mikael Perfekt, Mihai Putinar

Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors-Beurling transform acting on the associated Bergman space.…

math.FA2016★ 8 cited

Volterra operators on Hardy spaces of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt, Kristian Seip

For a Dirichlet series symbol $g (s) = \sum_{n \geq 1} b_{n} n^{- s}$ , the associated Volterra operator $T_{g}$ acting on a Dirichlet series $f (s) = \sum_{n \geq 1} a_{n} n^{- s}$ is d…

math.FA2015★ 8 cited

Weak product spaces of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

Let $H^{2}$ denote the space of ordinary Dirichlet series with square summable coefficients, and let $H_{0}^{2}$ denote its subspace consisting of series vanishing at…

math.FA2015★ 23 cited

Operator-Lipschitz estimates for the singular value functional calculus

Fredrik Andersson, Marcus Carlsson, Karl-Mikael Perfekt

We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and suff…

A Fejér--Riesz inequality for Dirichlet series

Recovering Product BMO from Schatten Hankel operators

Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions

Cyclicity and iterated logarithms in the Drury-Arveson space

Cyclicity in the Drury-Arveson space and other weighted Besov spaces

Correction to: Weak product spaces of Dirichlet series

Composition operators on weighted Hilbert spaces of Dirichlet series

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

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

The quasi-static plasmonic problem for polyhedra

Infinitely many embedded eigenvalues for the Neumann-Poincaré operator in 3D

A mean counting function for Dirichlet series and compact composition operators

The spectrum of some Hardy kernel matrices

Atomic decompositions, two stars theorems, and distances for the Bourgain-Brezis-Mironescu space and other big spaces

Norms of composition operators on the H2 space of Dirichlet series

On the spaces of bounded and compact multiplicative Hankel operators

Nehari's theorem for convex domain Hankel and Toeplitz operators in several variables

On the spectrum of the multiplicative Hilbert matrix

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

On Helson matrices: moment problems, non-negativity, boundedness, and finite rank

The essential spectrum of the Neumann--Poincare operator on a domain with corners

Volterra operators on Hardy spaces of Dirichlet series

Weak product spaces of Dirichlet series

Operator-Lipschitz estimates for the singular value functional calculus

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

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