📚  Bibliography

Uncertainty principle

• Donoho, Stark, Uncertainty principles and signal recovery, SIAM J. Appl. Math. 49, No. 3, 906-931 (1989). 

• Donoho, Stark, A note on rearrangements, spectral concentration, and the zero-order prolate spheroidal wavefunction, IEEE Trans. Inf. Theory 39, No. 1, 257-260 (1993).

• Folland, Sitaram, The uncertainty principle: A mathematical survey, J. Fourier Anal. Appl. 3, No. 3, 207-238 (1997). 

• Slepian, Some comments on Fourier analysis, uncertainty and modeling, SIAM Rev. 25, 379-393 (1983).

Coherent states

• Perelomov, Coherent States for Arbitrary Lie Group, Commun. Math. Phys. 26, 222-236 (1972). 

• Schupp, Wehrl entropy, coherent states and quantum channels, The physics and mathematics of Elliott Lieb. The 90th anniversary. Volume II. Berlin: European Mathematical Society (EMS), 329-344 (2022).

• Twareque Ali, Antoine, Gazeau, Mueller, Coherent states and their generalizations: A mathematical overview, Rev. Math. Phys. 7, No. 7, 1013-1104 (1995).

Concentration inequalities 

• Frank, Sharp inequalities for coherent states and their optimizers, Adv. Nonlinear Stud. 23, Article ID 20220050, 28 p. (2023).

• García-Ferrero, Ortega-Cerdá, Stability of the concentration inequality on polynomials, Commun. Math. Phys. 406, No. 5, Paper No. 112, 35 p. (2025).

• Gómez, Guerra, Ramos, Tilli, Stability of the Faber-Krahn inequality for the short-time Fourier transform, Invent. Math. 236, No. 2, 779-836 (2024).

• Gómez, Kalaj, Melentijević, Ramos, Uniform stability of concentration inequalities and applications, preprint (2024). 

• Kulikov, Nicola, Ortega-Cerdà, Tilli, A monotonicity theorem for subharmonic functions on manifolds, Adv. Math. 479, Part A, Article ID 110423, 18 p. (2025). 

• Nicola, Tilli, The Faber-Krahn inequality for the short-time Fourier transform, Invent. Math. 230, No. 1, 1-30 (2022).

• Ramos, Tilli, A Faber-Krahn inequality for wavelet transforms, Bull. Lond. Math. Soc. 55, No. 4, 2018-2034 (2023).  

Wehrl entropy conjecture

• Carlen, Some integral identities and inequalities for entire functions and their application to the coherent state transform, J. Funct. Anal. 97, No. 1, 231-249 (1991).

• Frank, Sharp inequalities for coherent states and their optimizers, Adv. Nonlinear Stud. 23, Article ID 20220050, 28 p. (2023).

• Frank, Nicola, Tilli, The generalized Wehrl entropy bound in quantitative form, preprint (2023).

• Kulikov, Functionals with extrema at reproducing kernels, Geom. Funct. Anal. 32, No. 4, 938-949 (2022).

• Kulikov, Nicola, Ortega-Cerdà, Tilli, A monotonicity theorem for subharmonic functions on manifolds, Adv. Math. 479,  Part A, Article ID 110423, 18 p. (2025).

• Lieb, Proof of an entropy conjecture of Wehrl, Commun. Math. Phys. 62, 35-41 (1978).

• Lieb, Solovej, Proof of an entropy conjecture for Bloch coherent spin states and its generalizations, Acta Math. 212, No. 2, 379-398 (2014).

• Wehrl, On the relation between classical and quantum-mechanical entropy, Rep. Math. Phys. 16, 353-358 (1979).