12 research outputs found
Incomplete inverse spectral and nodal problems for differential pencils
[[abstract]]We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子
An Introduction to Classical Inverse Eigenvalue Problems
Aim of these notes is to present an elementary introduction
to classical inverse eigenvalue problems in one dimension. Attention is mainly
focused on Sturm-Liouville differential operators given in canonical form
on a finite interval. A uniqueness result for a fourth order Euler-Bernoulli operator is also discussed
Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data
[[abstract]]The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]CH