Mathematics – Spectral Theory
Scientific paper
May 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983ap%26ss..92..105b&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 92, no. 1, May 1983, p. 105-112.
Mathematics
Spectral Theory
6
Convolution Integrals, Electromagnetic Spectra, Relativistic Electron Beams, Spectral Theory, Spectrum Analysis, Synchrotron Radiation, Bessel Functions, Emission Spectra, Inversions, Kernel Functions, Laplace Transformation, Numerical Stability, Radio Sources (Astronomy), White Noise
Scientific paper
The present investigation is concerned with the inversion and the noise properties of synchrotron spectra, taking into account situations in which the source region comprises a magnetic field B and an isotropic electron velocity distribution both of which are homogeneous. The synchrotron power radiated from the source per steradian per unit frequency range is considered. The formal inversion formula for the obtained transform is derived, and its properties are discussed. The formal inversion formula enables derivation of electron spectra from a wide range of suitable analytic forms. It is also a useful basis for an analysis regarding the stability and uniqueness of the derivation of electron spectra from noisy synchrotron spectra. Approximate methods of inversion are also examined, giving attention to the Laplace transform approximations, and a solution in terms of integral moments. Smoothing and stability properties are also explored.
Brown John C.
Craig Donald I. Jr.
Melrose Donald B.
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