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Inhaltsangabe
Time-Frequency Analysis is a rich source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued only in engineering, but recently, and with the development of wavelet theory, it has emerged as a thriving field of applied mathematics. This title presents a systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honouring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e. the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements.
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Time-Frequency Analysis is a rich source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued only in engineering, but recently, and with the development of wavelet theory, it has emerged as a thriving field of applied mathematics. This title presents a systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honouring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e. the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements.
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