Harmonic Analysis In Phase Space

By S. Koch. 2016

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Minimal representations via Bessel operators (2011, background): “p Rk\{0} → O,xtxyields the trivial bundle over Rk\{0} and the corresponding sections correspond to odd functions on Rk. This gives the Schro¨dinger picture of the metaplectic representation (see e.g. [11]) and the statement is clear. Now let us return to the general scalar case. To integrate Wto a u”
Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, background): “As we mentioned at the beginning, we will not use these representations and refer the reader to [17] for details.”
Quantization on Nilpotent Lie Groups (2016, methodology): “As such, in this monograph we will deal with the Heisenberg group almost exclusively in the context of pseudo-differential operators, and we refer to excellent surveys of Folland [Fol77a] and Howe [How80] on the role played by the Heisenberg group in the theory of partial differential equations and ”
The Faber–Krahn inequality for the short-time Fourier transform (2021, background): “It is well known that V f is a complex-valued, real analytic, bounded function and is an isometry (see [27, 33, 41, 50]).”