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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 018 393 623  
Author(s):  
Yurko, Viacheslav:  
Shorttitle:  
Integral transforms connected with higherordere differential operators with a singularity.  
Source:  
Integral Transforms Spec. Funct. 13, No. 6, 497  511 (2002)  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
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:  