Nils Mikael Signal

• Chen, Yuanyuan; Signahl, Mikael & Toft, Joachim (2017). Factorizations and Singular Value Estimates of Operators with Gelfand–Shilov and Pilipović kernels. Journal of Fourier Analysis and Applications. ISSN 1069-5869. s. 1–33. doi: 10.1007/s00041-017-9542-x. Fulltekst i vitenarkiv Vis sammendrag

  We prove that any linear operator with kernel in a Pilipović or Gelfand–Shilov space can be factorized by two operators in the same class. We also give links on numerical approximations for such compositions. We apply these composition rules to deduce estimates of singular values and establish Schatten–von Neumann properties for such operators.

• Chen, Yuanyuan; Signahl, Mikael & Toft, Joachim (2017). Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces, Generalized Functions and Fourier Analysis. Birkhäuser Verlag. ISSN 9783319519104. s. 31–44. doi: 10.1007/978-3-319-51911-1_3. Fulltekst i vitenarkiv
• Signahl, Mikael & Toft, Joachim (2012). Mapping properties for the Bargmann transform on modulation spaces. Journal of Pseudo-Differential Operators and Applications. ISSN 1662-9981. 3(1), s. 1–30. doi: 10.1007/s11868-011-0039-0. Fulltekst i vitenarkiv Vis sammendrag

  We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions. We also present some consequences. For example we prove that the spectrum of the Harmonic oscillator is the same for all modulation spaces

• Signahl, Mikael & Toft, Joachim (2011). Remarks on mapping properties for the Bargmann transform on modulation spaces. Integral transforms and special functions. ISSN 1065-2469. 22(4-5), s. 359–366. doi: 10.1080/10652469.2010.541056. Fulltekst i vitenarkiv
• Øksendal, Bernt; Proske, Norbert Frank & Signahl, Mikael (2006). The Cauchy problem for the wave equation with Levy noise initial data. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 9, s. 249–270. Fulltekst i vitenarkiv
• Pettersson, Roger & Signahl, Mikael (2005). Numerical approximation for a white noise driven SPDE with locally bounded drift. Potential Analysis. ISSN 0926-2601. 22(4), s. 375–393. Fulltekst i vitenarkiv

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• Signahl, Mikael (2006). Variational solutions of Semilinear Wave Equations Driven by Fractional Brownian noise. Fulltekst i vitenarkiv
• Signahl, Mikael (2006). Variational solutions of Semilinear Wave Equations Driven by Fractional Brownian noise. Fulltekst i vitenarkiv
• Signahl, Mikael (2006). Variational solutions of semilinear wave equations driven by multiplicative fractional Brownian noise. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  This paper focuses on variational solutions of the Cauchy problem for a non- linear wave equation with space-time fractional Brownian noise driving force of Hurst index H.

• Signahl, Mikael (2005). Variational Solutions of Semilinear Wave Equations Driven by Fractional Brownian Noise. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  This paper focuses on variational solutions of the Cauchy problem for a nonlinear wave equation with space-time fractional Brownian noise driving force of Hurst index $H\in (1/2,1)$ and random initial data. It is shown that this problem has a unique solution which depends continuously on the random initial data.

• Øksendal, Bernt Karsten; Proske, Frank Norbert & Signahl, Mikael (2003). The Cauchy problem for the wave equation with Lévy noise initial data. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  In this paper we study the Cauchy problem for the wave equation with space-time Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C2-solution, which takes an explicit form. Our approach is based on the use of the Hermite transform.

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