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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 018 393 623
Author(s):
Yurko, Viacheslav:
Shorttitle:
Integral transforms connected with higher-ordere differential operators with a singularity.
Source:
Integral Transforms Spec. Funct. 13, No. 6, 497 - 511 (2002)
Classification:
44A15Special transforms Legendre, Hilbert, etc.
Primary Classification:
34L10Eigenfunction expansions, completeness of eigenfunctions
Secondary Classification:
47E05Ordinary differential operators
34B20Weyl theory and its generalizations
Keywords:
differential equation with a singularity; boundary value problem; spectrum; completeness theorem; expansion convergence theorem
Review:

The key result is that the system of eigen- and associated functions
in a certain class L of boundary value problems is complete in a
certain Banach space of functions on an interval (0,T). The gist of
the paper (which is a continuation of the lasting author's research
in this direction) lies in the admission of a strong singularity in
differential equation at a point x=a within the interval (0,T),
compensated by certain ``matching" conditions imposed at the singular
point. The spectra and properties of expansions (e.g., uniformity of
convergence) are studied in detail.
Remarks to the editors:

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