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Extremals of Some Uncertainty Inequalities
Author(s) -
Morpurgo Carlo
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.1.52
Subject(s) - mathematics , inequality , constant (computer programming) , type (biology) , pure mathematics , calculus (dental) , mathematical economics , mathematical analysis , medicine , ecology , dentistry , computer science , biology , programming language
We characterize the extremal functions for Heisenberg type inequalities of the form‖ f ‖ 1 γ‖ f ‖ 2 δ ⩽ C ‖ | x | 2 f ‖ 1 α‖ | ξ | f ^ ‖ 2 β .The method also yields an alternative and elementary derivation of the sharp constant in Nash's inequality, originally found by Carlen and Loss.