Multiscale unique continuation properties of eigenfunctions (CROSBI ID 55575)
Prilog u knjizi | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Borisov, Denis ; Nakić, Ivica ; Rose, Christian ; Tautenhahn, Martin ; Veselić, Ivan
engleski
Multiscale unique continuation properties of eigenfunctions
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schrodinger operators and control theory. We review recent results and announce new ones regarding quantitative unique continuation principles for partial differential equations with an underlying multiscale structure. They concern Schrödinger and second order elliptic operators. An important feature is that the estimates are scale free and with quantitative dependence on parameters. These unique continuation principles apply to functions satisfying certain ‘rigidity’ conditions, namely that they are solutions of the corresponding elliptic equations, or projections on spectral subspaces. Carleman estimates play an important role in the proofs of these results.
scale free unique continuation property, equidistribution property, observability estimate, uncertainty relation, Carleman estimate, Schrödinger operator, elliptic differential equation.
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Podaci o prilogu
107-118.
objavljeno
10.1007/978-3-319-18494-4_7
Podaci o knjizi
Operator semigroups meet complex analysis, harmonic analysis and mathematical physics
Arendt, Wolfgang ; Chill, Ralph ; Tomilov, Yuri
Basel: Springer
2015.
978-3-319-18493-7