Variations on uncertainty principles for integral operators

References

• Amrein WO, Berthier AM. On support properties ofL p-functions and their Fourier transforms. J. Funct. Anal. 1977;24:258–267.
   Web of Science ®Google Scholar
• Balila EA, Reyes NN. Weighted uncertainty principles inL∞. J. Approx. Theory. 2000;106:241–248.
   Web of Science ®Google Scholar
• Benedicks M. On Fourier transforms of functions supported on sets of finite Lebesgue measure. J. Math. Anal. Appl. 1985;106:180–183.
   Web of Science ®Google Scholar
• Benedetto JJ. Frame decompositions, sampling, and uncertainty principle inequalities, wavelets: mathematics and applications. Stud. Adv. Math. Boca Raton, FL: CRC; 1994. pp. 247–304.
   Google Scholar
• Ben Saïd S, Kobayashi T, Ørsted B. Laguerre semigroup and Dunkl operators. Compos. Math. 2012;148:1265–1336.
   Google Scholar
• Betancor JJ, Stempak K. Relating multipliers and transplantation for Fourier-Bessel expansions and Hankel transform. Tohoku Math. J. 2001;53:109–129.
   Web of Science ®Google Scholar
• Bonami A, Demange B. A survey on uncertainty principles related to quadratic forms. Collect. Math. 2006;2:1–36.
   Google Scholar
• Carlson F. Une inégalité. Ark. Mat. Astr. Fysik. 1934;25B:1–5.
   Google Scholar
• Carlen EA, Loss M. Sharp constant in Nash’s inequality. Amer. J. Math. 1993;7:213–215.
   Google Scholar
• Cowling MG, Price JF. Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality. SIAM J. Math. Anal. 1984;15:151–165.
   Web of Science ®Google Scholar
• Jeu MFE. An uncertainty principle for integral operators. J. Funct. Anal. 1994;122:247–253.
   Web of Science ®Google Scholar
• Jeu MFE. The Dunkl transform. Invent. Math. 1993;113:147–162.
   Web of Science ®Google Scholar
• Dunkl CF. Differential-difference operators associated to reflection groups. Trans. Amer. Math. Soc. 1989;311:167–183.
   Web of Science ®Google Scholar
• Dunkl CF. Integral kernels with reflection group invariance. Can. J. Math. 1991;43:1213–1227.
   Web of Science ®Google Scholar
• Donoho DL, Stark PB. Uncertainty principles and signal recovery. SIAM J. Appl. Math. 1989;49:906–931.
   Web of Science ®Google Scholar
• Faris WG. Inequalities and uncertainty inequalities. J. Math. Phys. 1978;19:461–466.
   Web of Science ®Google Scholar
• Folland GB, Sitaram A. The uncertainty principle - a mathematical survey. J. Fourier Anal. Appl. 1997;3:207–238.
   Web of Science ®Google Scholar
• Ghobber S. Uncertainty principles involving L1norms for the Dunkl transform. Integral Transforms Spec. Funct. 2012. doi:10.1080/10652469.2012.712533.
   Google Scholar
• Ghobber S, Jaming P. Uncertainty principles for integral operators. ArXiv: 1206.1195v1 [math.CA]; 6 June 2012.
   Google Scholar
• Havin V, Jöricke B. The uncertainty principle in harmonic analysis. Berlin: Springer-Verlag; 1994.
   Google Scholar
• Humphreys JE. Reflection groups and Coxeter groups. Cambridge Stud. Adv. Math. 29. Cambridge: Cambridge University Press; 1990.
   Google Scholar
• Laeng E, Morpurgo C. An uncertainty inequality involving L1-norms. Proc. Amer. Math. Soc. 1999;127:3565–3572.
   Web of Science ®Google Scholar
• Lapointe L, Vinet L. Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 1996;178:425–452.
   Web of Science ®Google Scholar
• Larsson L, Maligranda L, Pečarić J, Persson L-E. Multiplicative inequalities of Carlson type and interpolation. Hackensack, NJ: World Scientific Publishing Co. Pty. Ltd.; 2006.
   Google Scholar
• Levin VI. Exact constants in inequalities of the Carlson type. Doklady Akad. Nauk SSSR (N.S.). 1948;59:635–638.
   Google Scholar
• Morpurgo C. Extremals of some uncertainty inequalities. Bull. London Math. Soc. 2001;33:52–58.
   Web of Science ®Google Scholar
• Nash J. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 1958;80:931–954.
   Web of Science ®Google Scholar
• Nowak A, Szarek TZ. Calderón-Zygmund operators related to Laguerre function expansions of convolution type. J. Math. Anal. Appl. 2012;388:801–816.
   Web of Science ®Google Scholar
• Polychronakos AP. Exchange operator formalism for integrable systems of particles. Phys. Rev. Lett. 1992;69:703–705.
   PubMed Web of Science ®Google Scholar
• Price JF. Inequalities and local uncertainty principles. J. Math. Phys. 1983;24:1711–1714.
   Web of Science ®Google Scholar
• Price JF. Sharp local uncertainty principles. Studia Math. 1987;85:37–45.
   Web of Science ®Google Scholar
• Price JF, Racki PC. Local uncertainty inequalities for Fourier series. Proc. Amer. Math. Soc. 1985;93:245–251.
   Web of Science ®Google Scholar
• Price JF, Sitaram A. Local uncertainty inequalities for locally compact groups. Trans. Amer. Math. Soc. 1988;308:105–114.
   Web of Science ®Google Scholar
• Price JF, Sitaram A. Local uncertainty inequalities for compact groups. Proc. Amer. Math. Soc. 1988;103:441–447.
   Web of Science ®Google Scholar
• Strichartz RS. Uncertainty principles in harmonic analysis. J. Funct. Anal. 1989;84:97–114.
   Web of Science ®Google Scholar
• Tuan VK, Yakubovich S. Donoho-Stark and Paley-Wiener theorems for the G-transform. Adv. Appl. Math. 2010;45:108–124.
   Web of Science ®Google Scholar
• Yakubovich SB. Luchko YuF. The hypergeometric approach to integral transforms and convolutions. Dordrecht: Kluwer; 1994.
   Google Scholar