Browsing NTNU Open by Author "Seip, Kristian"
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Approximation numbers of composition operators on H^p spaces of Dirichlet series
Bayart, Frederic; Queffelec, Herve; Seip, Kristian (Journal article; Peer reviewed, 2016)By a theorem of the first named author, $\varphi $ generates a bounded composition operator on the Hardy space ${\mathscr{H}}^p$of Dirichlet series $(1\le p<\infty )$ only if $\varphi (s)=c_0 s+\psi (s)$, where $c_0$ is a ... 
Contractive inequalities for Hardy spaces
Brevig, Ole Fredrik; OrtegaCerdà, Joaquim; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical Hp spaces of the unit disc. We study both coefficient estimates in terms of weighted ℓ 2 sums ... 
Convergence of series of dilated functions and spectral norms of GCD matrices
Seip, Kristian; Aistleitner, Christoph; Berkes, Istvan; Weber, Michel (Journal article; Peer reviewed, 2015) 
A converse to the Schwarz lemma for planar harmonic maps
Brevig, Ole Fredrik; OrtegaCerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2021)A sharp version of a recent inequality of Kovalev and Yang on the ratio of the (H1)∗ and H4 norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for ... 
Decay rates for approximation numbers of composition operators
Queffelec, Herve; Seip, Kristian (Journal article; Peer reviewed, 2015)A general method for estimating the approximation numbers of composition operators on the Hardy space H 2, using finitedimensional model subspaces, is studied and applied in the case when the symbol of the operator maps ... 
Extreme values of the Riemann zeta function and its argument
Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2018)We combine our version of the resonance method with certain convolution formulas for ζ(s) and logζ(s) . This leads to a new Ω result for ζ(1/2+it) : The maximum of ζ(1/2+it) on the interval 1≤t≤T is at ... 
A footnote to a theorem Halász
Saias, Eric; Seip, Kristian (Journal article; Peer reviewed, 2020)We study multiplicative functions f satisfying f(n)≤1 for all n, the associated Dirichlet series F(s):=∑∞n=1f(n)n−s, and the summatory function Sf(x):=∑n≤xf(n). Up to a possible trivial contribution from the numbers ... 
Galtype GCD sums beyond the critical line
Bondarenko, Andrii; Hilberdink, Titus; Seip, Kristian (Journal article; Peer reviewed, 2016) 
GCD sums and complete sets of squarefree numbers
Seip, Kristian; Bondarenko, Andrii (Journal article; Peer reviewed, 2015) 
GCD sums from Poisson integrals and systems of dilated functions
Aistleitner, Christoph; Berkes, Istvan; Seip, Kristian (Journal article; Peer reviewed, 2015) 
Hankel forms and Nehari's theorem
Søvik, Øistein (Master thesis, 2017)The purpose of this thesis is to explore the relation between the classical Hardy space of analytic functions and the Hardy space of Dirichlet series. Two chapters are devoted to developing the basic properties of these ... 
Helson's problem for sums of a random multiplicative function
Seip, Kristian; Bondarenko, Andriy (Journal article; Peer reviewed, 20161021)We consider the random functions $S_{N}(z):=\sum _{n=1}^{N}z(n)$SN(z):=∑Nn=1z(n), where $z(n)$z(n) is the completely multiplicative random function generated by independent Steinhaus variables $z(p)$z(p). It is shown that ... 
Hilberttransformpar og negativ brytning
LindJohansen, Øyvind (Master thesis, 2006)I løpet av de siste årene har det blitt mulig å lage medier som har permittivitet $epsilon_r=chi_e+1$ og permeabilitet $mu_r=chi_m+1$ med simultant negative realdeler. I slike medier vil man få negativ brytning og dette ... 
Large greatest common divisor sums and extreme values of the Riemann zeta function
Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2017) 
Linear space properties of H^p spaces of Dirichlet series
Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian (Journal article; Peer reviewed, 2019)We study H p spaces of Dirichlet series, called H p , for the range 0 < p < ∞. We begin by showing that two natural ways to define H p coincide. We then proceed to study some linear space properties of H p . More specifically, ... 
Moments of Random Multiplicative Functions and Truncated Characteristic Polynomials
Lindqvist, Sofia Margareta (Master thesis, 2015)An asymptotic formula for the 2kth moment of a sum of multiplicative Steinahus variables is given. This is obtained by expressing the moment as a 2kfold complex contour integral, from which one can extract the lead ing ... 
Note on the resonance method for the Riemann zeta function
Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2018)We improve Montgomery’s Ωresults for ζ(σ + it) in the strip 1/2 σ 1 and give in particular lower bounds for the maximum of ζ(σ+it) on √ T ≤ t ≤ T that are uniform in σ. We give similar lower bounds for the maximum of ... 
Operator theory in spaces of Dirichlet series
Brevig, Ole Fredrik (Doctoral theses at NTNU;2017:193, Doctoral thesis, 2017) 
Pseudomoments of the Riemann zeta function
Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)The 2kth pseudomoments of the Riemann zeta function ζ ( s ) are, following Conrey and Gamburd, the 2 k th integral moments of the partial sums of ζ ( s ) on the critical line. For fixed k > 1 / 2 , these moments are known ... 
Real time ultrasound simulation: Application to a medical training simulator
Bø, Lars Eirik (Master thesis, 2008)As ultrasound technology today finds new applications and becomes available to more and more users, the demand for good training procedures and material increases. This has motivated a research project aimed at developing ...