Special Issue "Joseph Fourier 250th Birthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (31 October 2018).
A printed edition of this Special Issue is available here.
Interests: Lie group thermodynamics; exponential families; representation theory; Lie group statistics; Lie group machine learning
Special Issues and Collections in MDPI journals
Special Issue in Entropy: Differential Geometrical Theory of Statistics
Special Issue in Entropy: Topological and Geometrical Structure of Information. Selected Papers from CIRM conferences 2017
Special Issue in Entropy: Statistical Distances and Geometry—Selected Papers from GSI conference 2017
Special Issue in Entropy: Lie Group Machine Learning and Lie Group Structure Preserving Integrators
For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation.
Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences.
The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in Geometric Mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.
A last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory.
The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.
Prof. Dr. Frédéric Barbaresco
Prof. Jean-Pierre Gazeau
Manuscript Submission Information
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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.