TY - JOUR

T1 - On Inverse Dynamical and Spectral Problems for the Wave and Schrӧdinger Equations on Finite Trees. The Leaf Peeling Method

AU - Avdonin, S. A.

AU - Mikhaylov, V. S.

AU - Nurtazina, K. B.

PY - 2017/8/17

Y1 - 2017/8/17

N2 - Interest in inverse dynamical, spectral, and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum applications. Recently a new effective leaf peeling method has been proposed by S. Avdonin and P. Kurasov for solving inverse problems on trees (graphs without cycles). It allows recalculating efficiently the inverse data from the original tree to smaller trees, “removing” leaves step by step up to the rooted edge. In this paper, the main step of the spectral and dynamical versions of the peeling algorithm, i.e., recalculating the inverse data for a “peeled tree” is described. Bibliography: 12 titles.

AB - Interest in inverse dynamical, spectral, and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum applications. Recently a new effective leaf peeling method has been proposed by S. Avdonin and P. Kurasov for solving inverse problems on trees (graphs without cycles). It allows recalculating efficiently the inverse data from the original tree to smaller trees, “removing” leaves step by step up to the rooted edge. In this paper, the main step of the spectral and dynamical versions of the peeling algorithm, i.e., recalculating the inverse data for a “peeled tree” is described. Bibliography: 12 titles.

UR - http://www.scopus.com/inward/record.url?scp=85019570158&partnerID=8YFLogxK

U2 - 10.1007/s10958-017-3388-2

DO - 10.1007/s10958-017-3388-2

M3 - Article

AN - SCOPUS:85019570158

SP - 1

EP - 10

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

ER -