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On unique continuation for Schrödinger operators of fractional and higher orders
Author(s) -
Seo Ihyeok
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.201300008
Subject(s) - continuation , mathematics , operator (biology) , schrödinger's cat , property (philosophy) , class (philosophy) , function (biology) , analytic continuation , range (aeronautics) , pure mathematics , mathematical analysis , mathematical physics , biochemistry , chemistry , repressor , artificial intelligence , evolutionary biology , biology , computer science , transcription factor , gene , programming language , philosophy , materials science , epistemology , composite material
In this note we study the property of unique continuation for solutions of| ( − Δ )α / 2u | ≤ | V u | , where V is in a function class of potentials including⋃ p > n / αL p ( R n )for n − 1 ≤ α < n . In particular, when n = 2 , our result gives a unique continuation theorem for the fractional ( 1 < α < 2 ) Schrödinger operator( − Δ ) α / 2 + V ( x )in the full range of α values.