• 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, 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 ...
    • Hilbert points in Hardy spaces 

      Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2023)
    • Hilberttransformpar og negativ brytning 

      Lind-Johansen, 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 ...
    • Idempotent Fourier multipliers acting contractively on Hp spaces 

      Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2021)
      We describe the idempotent Fourier multipliers that act contractively on Hp spaces of the d-dimensional torus Td for d≥1 and 1≤p≤∞. When p is not an even integer, such multipliers are just restrictions of contractive ...
    • 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, ...
    • Maximal norm Hankel operators 

      Brevig, Ole Fredrik; Seip, Kristian (Peer reviewed; Journal article, 2024)
    • Modular forms and Δ 

      Thrane, Thomas Agung Dibpa Anandita (Bachelor thesis, 2022)
      Modulære former dukker opp i mange matematiske grener som topologi, tallteori, kompleksanalyse, gruppeteori, og algebraisk geometri. For eksempel, så ble de brukt i Andrew Wiles sitt bevis av Fermats siste teorem. De har ...
    • 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 2k-fold 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 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 

      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 ...
    • Riesz projection and bounded mean oscillation for Dirichlet series 

      Konyagin, Sergei; Queffelec, Herve; Saksman, Eero; Seip, Kristian (Peer reviewed; Journal article, 2022)
      We prove that the norm of the Riesz projection from L∞(Tn) to Lp(Tn) is 1 for all n≥1 only if p≤2, thus solving a problem posed by Marzo and Seip in 2011. This shows that Hp(T∞) does not contain the dual space of H1(T∞) ...
    • Sampling on Quasicrystals 

      Grepstad, Sigrid (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 

      Teklehaymanot, Nigus Girmay (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 

      Brevig, Ole Fredrik; Perfekt, Karl-Mikael; Seip, Kristian; Siskakis, Aristomenis; Vukotic, Dragan (Journal article; Peer reviewed, 2016)
    • The Riemann hypothesis, The Lindelöf hypothesis and the density hypothesis - consequences and relations 

      Dalaker, Lars (Bachelor thesis, 2020)
      I denne artikkelen vil me drøfte nokre viktige eigenskapar til Riemanns zeta-funksjon. Me vil ta ta for oss den berømte Riemann-hypotesen, i tillegg til Lindelöf-hypotesen og tettleikshypotesen, og samanhengen mellom desse. ...
    • The Sidon Constant for Ordinary Dirichlet Series 

      Brevig, Ole Fredrik (Master thesis, 2013)
      We obtain the asymptotic formula of the Sidon constant for ordinary Dirichlet series using the Bohnenblust--Hille inequality and estimates on smooth numbers. We moreover give precise estimates for the error term.