Geodesic
On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 7-21

Voir la notice de l'article provenant de la source Math-Net.Ru

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 the smaller trees, ‘removing’ leaves step by step up to the rooted edge. In this paper we describe the main step of the spectral and dynamical versions of the peeling algorithm – recalculating the inverse data for the ‘peeled tree’. 
@article{ZNSL_2015_438_a0,
     author = {S. A. Avdonin and V. S. Mikhaylov and K. B. Nurtazina},
     title = {On inverse dynamical and spectral problems for the wave and {Schr\"odinger} equations on finite trees. {The} leaf peeling method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--21},
     publisher = {mathdoc},
     volume = {438},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a0/}
}
TY  - JOUR
AU  - S. A. Avdonin
AU  - V. S. Mikhaylov
AU  - K. B. Nurtazina
TI  - On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 7
EP  - 21
VL  - 438
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a0/
LA  - en
ID  - ZNSL_2015_438_a0
ER  - 
%0 Journal Article
%A S. A. Avdonin
%A V. S. Mikhaylov
%A K. B. Nurtazina
%T On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 7-21
%V 438
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a0/
%G en
%F ZNSL_2015_438_a0
S. A. Avdonin; V. S. Mikhaylov; K. B. Nurtazina. On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 7-21. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a0/