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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 018 799 772
Author(s):
Zhidkov, Peter E.:
Shorttitle:
An analog of the Fourier transform associated with a nonlinear one-dimensional Schroedinger equation
Source:
Nonlinear Anal., Theory Methods Appl, 52A, No. 3, 737-754 (2003)
Classification:
34L10Eigenfunction expansions, completeness of eigenfunctions
Primary Classification:
34L30Nonlinear ordinary differential operators
Secondary Classification:
42C30Completeness of sets of functions
47J10Nonlinear eigenvalue problems
Keywords:
nonlinear Schroedinger equation on half line; eigenfunction expanion; continuous spectrum; completeness of eigenfunctions; Fourier transform
Review:

Author summarizes the last five years of his research and ``grey" as
well as standard publication activity on the subject where his
attention has been paid to the completeness of the set of solutions
of a class of nonlinear Sturm-Liouville problems on the half-axis
under certain technical assumptions (not weakened to an extreme yet).
Being inspired by the idea that the kernel of the well known Fourier
integral transformation (in various versions) satisfies always a
linear Sturm-Liouvillean problem, the author emphasizes that the core
of his new result lies in teh availability of an estimate of the
bounds (4) valid for his ``generalized Fourier transform" of any
function from a certain Schwartz space.
Remarks to the editors:

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