Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century

• Main Author: Gazeau, Jean-Pierre (auth)
• Other Authors: Barbaresco, Frédéric (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: signal processing; thermodynamics; heat pulse experiments; quantum mechanics; variational formulation; Wigner function; nonholonomic constraints; thermal expansion; homogeneous spaces; irreversible processes; time-slicing; affine group; Fourier analysis; non-equilibrium processes; harmonic analysis on abstract space; pseudo-temperature; stochastic differential equations; fourier transform; Lie Groups; higher order thermodynamics; short-time propagators; discrete thermodynamic systems; metrics; heat equation on manifolds and Lie Groups; special functions; poly-symplectic manifold; non-Fourier heat conduction; homogeneous manifold; non-equivariant cohomology; Souriau-Fisher metric; Weyl quantization; dynamical systems; symplectization; Weyl-Heisenberg group; Guyer-Krumhansl equation; rigged Hilbert spaces; Lévy processes; Born-Jordan quantization; discrete multivariate sine transforms; continuum thermodynamic systems; interconnection; rigid body motions; covariant integral quantization; cubature formulas; Lie group machine learning; nonequilibrium thermodynamics; Van Vleck determinant; Lie groups thermodynamics; partial differential equations; orthogonal polynomials
• Online Access: DOAB: download the publication; DOAB: description of the publication

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...