Blar i NTNU Open på forfatter "Malinnikova, Eugenia"

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    • An improvement of the Kolmogorov-Riesz compactness theorem 

      Hanche-Olsen, Harald; Holden, Helge; Malinnikova, Eugenia (Journal article; Peer reviewed, 2018)
      The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces.

    • Construction of Salem Sets 

      Samuelsen, Helge Jørgen (Master thesis, 2021)
      I denne oppgaven vil vi utforske salemmengder. En salemmengde er en borelmengde hvor hausdorffdimensjonen tilsvarer fourierdimensjonen. Det er kjent at hausdorffdimensjonen er begrenset nedenfra av fourierdimensjonen, og ...

    • Covering theorems in analysis and their applications 

      Buzaljko, Amra (Master thesis, 2017)
      In this thesis, we study three classical covering results in analysis; the Vitali covering lemma, the Besicovitch covering lemma and the Vitali covering theorem. We exploit the ordering structure of the real line to obtain ...

    • Dynamical versions of Hardy's uncertainty principle: a survey. 

      Malinnikova, Eugenia; Fernandez-Bertolin, Aingeru (Peer reviewed; Journal article, 2021)
      Abstract: The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, ...

    • Fourierhyperfunksjoner 

      Maria Kristine, Skartsæterhagen (Master thesis, 2008)
      Oppgaven handler om fouriertransformasjon av generaliserte funksjoner, med spesiell vekt på fouriertransformasjon av hyperfunksjoner. Transformasjonen på hyperfunksjoner er deretter sammenlignet med Carlemans fouriertransform, ...

    • Inequalities in Hilbert Spaces 

      Wigestrand, Jan (Master thesis, 2008)
      The main result in this thesis is a new generalization of Selberg's inequality in Hilbert spaces with a proof. In Chapter 1 we define Hilbert spaces and give a proof of the Cauchy-Schwarz inequality and the Bessel inequality. ...

    • Kingman's subadditive ergodic theorem and its application 

      Haugsand, Erling Brækhus (Master thesis, 2017)
      In this master thesis we study Kingman's subadditive ergodic theorem and its application. We prove Kingman's theorem based on a proof by Steel. We also study two major applications of Kingman's theorem, convergence of ...

    • Lecture notes on quantitative unique continuation for solutions of second order elliptic equations 

      Malinnikova, Eugenia; Logunov, Alexander (Chapter, 2020)
      In these lectures we present some useful techniques to study quantitative properties of solutions of elliptic PDEs. Our aim is to outline the proof of a recent result on propagation of smallness. The ideas are also useful ...

    • Mathematical Model of the Geomagnetic Field 

      Thorsen, Kjetil (Master thesis, 2006)
      First comes a description of a mathematical model of the geomagnetic field. Then some discussion of the classical non-uniqueness results of Backus. Further we look at more recent results concerning reconstruction of the ...

    • Nodal Geometry and Growth of Solutions to Elliptic Partial Differential Equations 

      Decio, Stefano (Doctoral theses at NTNU;2022:216, Doctoral thesis, 2022)
      In this thesis we will study zeros and growth properties of solutions to elliptic PDEs. In particular, we first study zeros of linear combination of Laplace-Beltrami eigenfunctions via a growth estimate for positive solutions ...

    • Norms and Eigenvalues of Time-Frequency Localization Operators 

      Knutsen, Helge (Master thesis, 2018)
      In this report we study and compare two types of time-frequency localization operators, the first is based on composition of projections in time and frequency, and the second is Daubechies' localization operator. We provide ...

    • On the Three Ball Theorem for Solutions of the Helmholtz Equation 

      Berge, Stine Marie; Malinnikova, Eugenia (Journal article, 2021)
      Let $u_k$ be a solution of the Helmholtz equation with the wave number $k$, $\Delta u_k+k^2 u_k=0$, on (a small ball in) either $\mathbb{R}^n$, $\mathbb{S}^n$, or $\mathbb{H}^n$. For a fixed point $p$, we define ...

    • Product of Hyperfunctions with Disjoint Support 

      Eikrem, Kjersti Solberg (Master thesis, 2008)
      We prove that if two hyperfunctions on the unit circle have disjoint support, then the convolution of their Fourier coefficients multiplied with a weight is zero when the weight goes to 1. We prove this by using the ...

    • Quantitative Unique Continuation and Eigenvalue Bounds for the Laplacian 

      Berge, Stine Marie (Doctoral theses at NTNU;2021:285, Doctoral thesis, 2021)
      I denne avhandlingen skal vi studere flere aspekter ved laplaceoperatoren, spesielt med hensyn på egenverdier og egenfunksjoner. En stor del av avhandlingen er dedikert til kvantitativ unik utvidelse ulikheter for harmoniske ...

    • Two types of Rubio de Francia operators on Triebel-Lizorkin and Besov spaces 

      Malinnikova, Eugenia; Osipov, Nikolay N. (Peer reviewed; Journal article, 2018)
      We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014) and answering Havin’s question to one of the authors. ...

    • Uncertainty Principles in Time-Frequency Analysis – Fractals and Schrödinger Evolutions 

      Knutsen, Helge (Doctoral theses at NTNU;2023:162, Doctoral thesis, 2023)
      In this thesis we study two uncertainty principles from the perspective of timefrequency analysis. The first part, to which a significant portion is dedicated, is concerned with deriving an analog in the joint time-frequency ...

    • Zeros of the Wigner distribution and the short-time Fourier transform 

      Grochenig, Karlheinz; Jaming, Philippe; Malinnikova, Eugenia (Peer reviewed; Journal article, 2019)
      We study the question under which conditions the zero set of a (cross-) Wigner distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will ...