A solution is given to a conjecture proposed recently by Y. Wigderson and A. Wigderson concerning a “Heisenberg-like” uncertainty principle. That conjecture is about the image of the map f?fqf?qf2f?2,f∈??0,documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ fmapsto frac{{leftVert frightVert}_q{leftVert overset{frown }{f}rightVert}_q}{{leftVert frightVert}_2{leftVert overset{frown }{f}rightVert}_2},fin ell left(mathbb{R}right)backslash left{0right}, $$end{document} where ?(?) stands for the Schwartz class of functions on the real line. Also, a more general question is answered, where the L2 norm is replaced by the Lp norm in the denominator.
展开▼
