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Semi‐classical resolvent estimates and regions free of resonances
Author(s) -
Vodev Georgi
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300018
Subject(s) - resolvent , mathematics , resolvent formalism , variable (mathematics) , mathematical analysis , pure mathematics , banach space , finite rank operator
We prove resolvent estimates for self‐adjoint operators of the form P ( h ) = − h 2 Δ + V ( x , h )onL 2 ( R n ) , n ≥ 3 , where 0 < h ≪ 1 is a semi‐classical parameter and V = O ( h ν ) , ν > 0 , is a real‐valued potential. The potential is supposed to have very little regularity with respect to the radial variable, only. As a consequence, we obtain a region free of resonances in the case when V is of compact support.