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has been cited by the following article:

• TITLE: The AK Transform

  AUTHORS: Altair S. de Assis, Siegbert Kuhn, Juan A. Limaco

  KEYWORDS: Integral Transform, Lebesgue Measures, Kinetic Theory of Bounded Plasmas, Natural Eigenmodes, Transport, Q-Machines, Plasma Diodes, Tokamak, Nuclear Fusion

  JOURNAL NAME: Applied Mathematics, Vol.8 No.2, February 10, 2017

  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].