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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| פורמט: | Online |
| שפה: | אנגלית |
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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| גישה מקוונת: | 32856 |
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| _version_ | 1869514229844803584 |
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| author | Gazeau, Jean-Pierre Barbaresco, Frédéric |
| author_browse | Barbaresco, Frédéric Gazeau, Jean-Pierre |
| author_facet | Gazeau, Jean-Pierre Barbaresco, Frédéric |
| author_sort | Gazeau, Jean-Pierre |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-50897 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-508972023-12-20T18:40:30Z Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century Gazeau, Jean-Pierre Barbaresco, Frédéric Q1-390 QC1-999 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 bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general 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. 2021-02-11T16:55:45Z 2021-02-11T16:55:45Z 2019-04-05 11:17:10 2019 book 32856 9783038977469 https://directory.doabooks.org/handle/20.500.12854/50897 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://play.google.com/books/publish/a/14935057684283403269#details/ISBN:9783038977469 https://mdpi.com/books/pdfview/book/1189 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03897-747-6 10.3390/books978-3-03897-747-6 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783038977469 260 open access |
| spellingShingle | Q1-390 QC1-999 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 bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general Gazeau, Jean-Pierre Barbaresco, Frédéric Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title | Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title_full | Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title_fullStr | Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title_full_unstemmed | Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title_short | Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst century |
| title_sort | joseph fourier 250th birthday modern fourier analysis and fourier heat equation in information sciences for the xxist century |
| topic | Q1-390 QC1-999 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 bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general |
| topic_facet | Q1-390 QC1-999 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 bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general |
| url | 32856 |
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