Naslov
Multiscale unique continuation properties of eigenfunctions

Autori
Borisov, Denis ; Nakić, Ivica ; Rose, Christian ; Tautenhahn, Martin ; Veselić, Ivan

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Operator semigroups meet complex analysis, harmonic analysis and mathematical physics

Urednik/ci
Arendt, Wolfgang ; Chill, Ralph ; Tomilov, Yuri

Izdavač
Springer

Grad
Basel

Godina
2015

Raspon stranica
107-118

ISBN
978-3-319-18493-7

Ključne riječi
scale free unique continuation property, equidistribution property, observability estimate, uncertainty relation, Carleman estimate, Schrödinger operator, elliptic differential equation.

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA