TY - BOOK
ID - 32856
TI - Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century
AU - Barbaresco, Frédéric
AU - Gazeau, Jean-Pierre
PB - MDPI - Multidisciplinary Digital Publishing Institute
PY - 2019
KW - Weyl-Heisenberg group
KW - affine group
KW - Weyl quantization
KW - Wigner function
KW - covariant integral quantization
KW - Fourier analysis
KW - special functions
KW - rigged Hilbert spaces
KW - quantum mechanics
KW - signal processing
KW - non-Fourier heat conduction
KW - thermal expansion
KW - heat pulse experiments
KW - pseudo-temperature
KW - Guyer-Krumhansl equation
KW - higher order thermodynamics
KW - Lie groups thermodynamics
KW - homogeneous manifold
KW - poly-symplectic manifold
KW - dynamical systems
KW - non-equivariant cohomology
KW - Lie group machine learning
KW - Souriau-Fisher metric
KW - Born–Jordan quantization
KW - short-time propagators
KW - time-slicing
KW - Van Vleck determinant
KW - thermodynamics
KW - symplectization
KW - metrics
KW - non-equilibrium processes
KW - interconnection
KW - discrete multivariate sine transforms
KW - orthogonal polynomials
KW - cubature formulas
KW - nonequilibrium thermodynamics
KW - variational formulation
KW - nonholonomic constraints
KW - irreversible processes
KW - discrete thermodynamic systems
KW - continuum thermodynamic systems
KW - fourier transform
KW - rigid body motions
KW - partial differential equations
KW - Lévy processes
KW - Lie Groups
KW - homogeneous spaces
KW - stochastic differential equations
KW - harmonic analysis on abstract space
KW - heat equation on manifolds and Lie Groups
SN - 9783038977469
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 -