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

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

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...

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Auteur principal: Gazeau, Jean-Pierre (auth)
Autres auteurs: Barbaresco, Frédéric (auth)
Format: Chapitre de livre
Publié: MDPI - Multidisciplinary Digital Publishing Institute 2019
Sujets:
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
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Résumé: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.
Description matérielle:1 electronic resource (260 p.)
ISBN:books978-3-03897-747-6
9783038977469
Accès:Open Access

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