Abstract
The incomplete inverse spectral and inverse nodal problems for Dirac operator defined on a finite interval with separated boundary conditions are considered. We prove uniqueness theorems for the so-called incomplete inverse spectral problem. Using the obtained result we show that for a unique determination of the operator it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.
Highlights
Consider the eigenvalue problem corresponding to the Dirac operator, denoted by L := L(Q(x); α, β), of the form ly := By – Q(x)y = λy, < x
1 Introduction Consider the eigenvalue problem corresponding to the Dirac operator, denoted by L := L(Q(x); α, β), of the form ly := By – Q(x)y = λy, < x
In [ ] inverse nodal problems of reconstructing the Dirac operator on a finite interval were studied, where it was proved that the operator L is determined uniquely by specifying a dense set of nodal points
Summary
1 Introduction Consider the eigenvalue problem corresponding to the Dirac operator, denoted by L := L(Q(x); α, β), of the form ly := By – Q(x)y = λy, < x < , In [ ] inverse nodal problems of reconstructing the Dirac operator on a finite interval were studied, where it was proved that the operator L is determined uniquely by specifying a dense set of nodal points.
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