The AK Transform

Download Download as PDF (Size:352KB)  HTML   XML  PP. 145-153  
DOI: 10.4236/am.2017.82012    298 Downloads   423 Views  

ABSTRACT

In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded distribution functions such as in Q machines/plasma diodes or in the scrap-off layer of Tokamak fusion plasmas. The results are valid for functions of function spaces—Lebesgue spaces, which are defined using a natural generalization of the p-norm for finite-dimensional vector spaces, where is the real set, σs is the σ-algebra of Lebesgue measurable sets, and the μ Lebesgue measure. , so that . Note that, using a simpler notation, more natural/known to engineers, f could be considered any piecewise continuous function, that is: Here is a Euclidian space with the usual norm (inner product: ) given by: [1].

Cite this paper

de Assis, A. , Kuhn, S. and Limaco, J. (2017) The AK Transform. Applied Mathematics, 8, 145-153. doi: 10.4236/am.2017.82012.

References

[1] Rana, I.K. (2002) An Introduction to Measure and Integration, Second Edition, Graduate Studies in Mathematics, Volume 45, American Mathematical Society, Providence, Rhode Island, USA.
https://doi.org/10.1090/gsm/045
[2] Santiago, M.A.M., de Assis, A.S., Kuhn, S. and Schupfer, N. (1994) Ion-Acoustic Eigenmodes in a Collisionless Bounded Plasma. Brazilian Journal of Physics, 24, 699-703.
[3] Kuhn, S. (1984) Linear Longitudinal Eigenmodes in Collisionless Plasma Diodes with Thin Sheaths. Part I. Method. Physics of Fluids, 27, 1821.
https://doi.org/10.1063/1.864795
[4] Kuhn, S. (1984) Linear Longitudinal Eigenmodes in Collisionless Plasma Diodes with Thin Sheaths. Part II. Application to an Extended Pierce—Type Problem. Physics of Fluids, 27, 1821.
https://doi.org/10.1063/1.864796
[5] Schupfer, N., Kuhn, S., Santigo, M.A.M. and de Assis, A.S. (1991) External-Circuit Effects on Ion-Acoustic Eigenmodes in a Collisionless Bounded Plasma. 1991 International Workshop on Plasma Physics: Current Research on Fusion, Laboratory, and Astrophysical Plasmas, Pichl/Schladming, Austria, 28 February-2 March 1991, 131-136. Kuhn, S., Pedit, R., Rieser, H., Schupfer, N., Wertmann, H., Santigo, M.A.M. and de Assis, A.S. (1990) Some Lines of Research Currently Conducted by the Bounded Plasma Systems Group at Innsbruck University, International Workshop on Plasma Physics: Plasma Theoretical Problems in Astro- and Fusion Physics, Pichl/Schladm- ing, Austria, 1-3 March, 1990, 201-214.
[6] Kuhn, S., Schupfer, N., Santigo, M.A.M. and de Assis, A.S. (1990) Ion-Acoustic Eigenmodes in a Collisionless Bounded Plasma. 17th European Physical Society (EPS) Conference on Controlled Fusion and Plasma Heating, Amsterdam, 25-29 June 1990, 1786-1789.

  
comments powered by Disqus

Copyright © 2017 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.