TY - BOOK ID - 136128819 TI - Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century AU - Gazeau, Jean-Pierre AU - Barbaresco, Frédéric PY - 2019 PB - MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - signal processing KW - thermodynamics KW - heat pulse experiments KW - quantum mechanics KW - variational formulation KW - Wigner function KW - nonholonomic constraints KW - thermal expansion KW - homogeneous spaces KW - irreversible processes KW - time-slicing KW - affine group KW - Fourier analysis KW - non-equilibrium processes KW - harmonic analysis on abstract space KW - pseudo-temperature KW - stochastic differential equations KW - fourier transform KW - Lie Groups KW - higher order thermodynamics KW - short-time propagators KW - discrete thermodynamic systems KW - metrics KW - heat equation on manifolds and Lie Groups KW - special functions KW - poly-symplectic manifold KW - non-Fourier heat conduction KW - homogeneous manifold KW - non-equivariant cohomology KW - Souriau-Fisher metric KW - Weyl quantization KW - dynamical systems KW - symplectization KW - Weyl-Heisenberg group KW - Guyer-Krumhansl equation KW - rigged Hilbert spaces KW - Lévy processes KW - Born–Jordan quantization KW - discrete multivariate sine transforms KW - continuum thermodynamic systems KW - interconnection KW - rigid body motions KW - covariant integral quantization KW - cubature formulas KW - Lie group machine learning KW - nonequilibrium thermodynamics KW - Van Vleck determinant KW - Lie groups thermodynamics KW - partial differential equations KW - orthogonal polynomials UR - https://www.unicat.be/uniCat?func=search&query=sysid:136128819 AB - 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. One 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. ER -