Now showing items 1-20 of 21

• #### Approximation numbers of composition operators on H^p spaces of Dirichlet series ﻿

(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 ﻿

(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 ﻿

(Journal article; Peer reviewed, 2015)
• #### Decay rates for approximation numbers of composition operators ﻿

(Journal article; Peer reviewed, 2015)
A general method for estimating the approximation numbers of composition operators on the Hardy space H 2, using finite-dimensional 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 ﻿

(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 ...
• #### Gal-type GCD sums beyond the critical line ﻿

(Journal article; Peer reviewed, 2016)
• #### GCD sums and complete sets of square-free numbers ﻿

(Journal article; Peer reviewed, 2015)
• #### GCD sums from Poisson integrals and systems of dilated functions ﻿

(Journal article; Peer reviewed, 2015)
• #### Hankel forms and Nehari's theorem ﻿

(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 ﻿

(Journal article; Peer reviewed, 2016-10-21)
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 ﻿

(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 ﻿

(Journal article; Peer reviewed, 2017)
• #### Moments of Random Multiplicative Functions and Truncated Characteristic Polynomials ﻿

(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 2k-fold complex contour integral, from which one can extract the lead- ing ...
• #### Note on the resonance method for the Riemann zeta function ﻿

(Journal article; Peer reviewed, 2018)
We improve Montgomery’s Ω-results 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 ﻿

(Doctoral theses at NTNU;2017:193, Doctoral thesis, 2017)
• #### Pseudomoments of the Riemann zeta function ﻿

(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 ﻿

(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 ...
• #### Sampling on Quasicrystals ﻿

(Master thesis, 2011)
We prove that quasicrystals are universal sets of stable sampling in any dimension. Necessary and sufficient density conditions for stable sampling and interpolation sets in one dimension are studied in detail.
• #### Some Improved Estimates in the Dirichlet Divisor Problem from Bourgain's Exponent Pair ﻿

(Master thesis, 2018)
The thesis work is a survey of recent developments on the famous error terms in the Dirichlet divisor problem. We consider the power moments of the Riemann zeta-function in the critical strip and we managed to obtain some ...
• #### The multiplicative Hilbert matrix ﻿

(Journal article; Peer reviewed, 2016)