Abstract
For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization 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 (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.
Highlights
Key Technology Domain PCC (Processing, Control & Cognition) Representative, Thales Land & Air Systems, Voie Pierre-Gilles de Gennes, F91470 Limours, France
Fourier analysis and in MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation
XXth century has explored the generalization of Fourier modern development of Fourier analysis during XXth century has explored the generalization of and Fourier-Plancherel formulaformula for non-commutative harmonic analysis,analysis, applied to locallytocompact
Summary
MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier, who showed representing a function as a Fourier, who showed thatthat representing a function as a sum sum of trigonometric functions greatly simplifies the study of heat transfer and addresses classically of trigonometric functions greatly simplifies the study of heat transfer and addresses classically commutativeharmonic harmonicanalysis. Classicalcommutative commutativeharmonic harmonicanalysis analysisisisrestricted restrictedto to functions functions commutative n /Zn , Fourier defined on a topological locally compact and Abelian group. R defined on a topological locally compact and Abelian group G FourierFourier transform when Gwhen is a finite group).
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