Nonlinear inversion of a band-limited Fourier transform

Nonlinear inversion of a band-limited Fourier transform

Article history: Available online 3 May 2009 Communicated by Thomas Strohmer on 22 July 2008

Nonlinear Integrable Equations and Nonlinear Fourier Transform

In this paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Kortewegde Vries (KdV), the nonlinear Schrödinger (NLS) and the Davey-Stewartson (DS) equations. The solution of certain integrable equations in terms of formal power series was obtained in [4], [5]. In these papers the solution was expressed in a formal pow...

On Pointwise Inversion of the Fourier Transform of Bv0 Functions

Using a Riemann-Lebesgue lemma for the Fourier transform over the class of bounded variation functions that vanish at infinity, we prove the Dirichlet–Jordan theorem for functions on this class. Our proof is in the Henstock–Kurzweil integral context and is different to that of Riesz-Livingston [Amer. Math. Monthly 62 (1955), 434–437]. As consequence, we obtain the Dirichlet–Jordan theorem for f...

Experiences with a Ku-Band Microwave Fourier Transform Spectrometer

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

12 Invariant Nonlinear Correlations via Fourier Transform