The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.
Cubic Dirac operators are defined for infinite-dimensional color Lie algebras using Z-gradings to fix normal ordering, with corrections when a color Kac-Peterson class vanishes, yielding square formulas and applications to Kac-Moody superalgebras including Dirac inequalities.
The Wirtinger criterion cannot determine frame sets for odd functions at densities less than 2, including the first Hermite function.
citing papers explorer
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The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
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Cohomology of CR structures on compact Lie groups
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.
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Dirac operators for infinite-dimensional color Lie algebras
Cubic Dirac operators are defined for infinite-dimensional color Lie algebras using Z-gradings to fix normal ordering, with corrections when a color Kac-Peterson class vanishes, yielding square formulas and applications to Kac-Moody superalgebras including Dirac inequalities.
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On a fundamental barrier of the Wirtinger criterion for Gabor systems with odd functions
The Wirtinger criterion cannot determine frame sets for odd functions at densities less than 2, including the first Hermite function.