One-Dimensional Resampling with Inverse and Forward Mapping Functions

One-Dimensional Resampling with Inverse and Forward Mapping Functions

One-dimensional Inverse Limits with Set-valued Functions

In this paper we show that an inverse limit is 1-dimensional whenever the bonding functions are upper semi-continuous from [0, 1] into C([0, 1]) and dim(G(fi ◦ fi+1 ◦ · · · ◦ fj)) = 1 for all integers i and j, 1 ≤ i ≤ j. We apply this result to show that such an inverse limit is treelike and also to show that unions of certain finite collections of interval-valued upper semi-continuous function...

One - dimensional inverse scattering and spectral problems

Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results due to the author are presented. The classical results are often presented in a new way. Several highlights of the new results include: 1) Analysis of the invertibility of the steps in the Gel’fand-Levitan and Marchenko inversion procedures, 2) Theory of the inverse ...

One step forward

Inverse nodal problem for p-Laplacian with two potential functions

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...