LEADER 04779nam 2200889z- 450 001 9910346692703321 005 20231214133336.0 035 $a(CKB)4920000000094742 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/50897 035 $a(EXLCZ)994920000000094742 100 $a20202102d2019 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aJoseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century 210 $cMDPI - Multidisciplinary Digital Publishing Institute$d2019 215 $a1 electronic resource (260 p.) 311 $a3-03897-746-2 330 $aFor 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. 610 $asignal processing 610 $athermodynamics 610 $aheat pulse experiments 610 $aquantum mechanics 610 $avariational formulation 610 $aWigner function 610 $anonholonomic constraints 610 $athermal expansion 610 $ahomogeneous spaces 610 $airreversible processes 610 $atime-slicing 610 $aaffine group 610 $aFourier analysis 610 $anon-equilibrium processes 610 $aharmonic analysis on abstract space 610 $apseudo-temperature 610 $astochastic differential equations 610 $afourier transform 610 $aLie Groups 610 $ahigher order thermodynamics 610 $ashort-time propagators 610 $adiscrete thermodynamic systems 610 $ametrics 610 $aheat equation on manifolds and Lie Groups 610 $aspecial functions 610 $apoly-symplectic manifold 610 $anon-Fourier heat conduction 610 $ahomogeneous manifold 610 $anon-equivariant cohomology 610 $aSouriau-Fisher metric 610 $aWeyl quantization 610 $adynamical systems 610 $asymplectization 610 $aWeyl-Heisenberg group 610 $aGuyer-Krumhansl equation 610 $arigged Hilbert spaces 610 $aLévy processes 610 $aBorn?Jordan quantization 610 $adiscrete multivariate sine transforms 610 $acontinuum thermodynamic systems 610 $ainterconnection 610 $arigid body motions 610 $acovariant integral quantization 610 $acubature formulas 610 $aLie group machine learning 610 $anonequilibrium thermodynamics 610 $aVan Vleck determinant 610 $aLie groups thermodynamics 610 $apartial differential equations 610 $aorthogonal polynomials 700 $aGazeau$b Jean-Pierre$4auth$048964 702 $aBarbaresco$b Frédéric$4auth 906 $aBOOK 912 $a9910346692703321 996 $aJoseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century$93033492 997 $aUNINA