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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 016 852 173  
Author(s):  
Makin, A. S.:  
Shorttitle:  
On manypoint spectral boundary value problems.  
Source:  
Differ. Equ. 36, No. 10, 1461  1468 (2000); translation from Differ. Uravn. 36, No. 10, 1324  1330 (2000).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
Review:  
The growing role of the nonHermitian Hamiltonians in physics (the most fresh Los Alamos preprint arXiv: mathph/0205002 by B. Bagchi and C. Quesne may be recalled for review and typical illustration) is paralleled by a perceivable intensification of their rigorous studies. This represents a strong motivation for the study of the Laplace operator on a finite interval with the Dirichlet boundary condition at the mere left end. In the letter in question this operator is made nonselfadjoint via the generalized rightend boundary condition, complementing its usual mixed form by a strongly nonlocal term (viz, by a superposition of the first derivatives at an mplet of internal points). For the resulting BitsadzeSamarskii (or generalized SamarskiiIonkin) solutions (forming a biorthogonal basis in the corresponding Hilbert space) the author proves a bound for the norms and (sizes of) eigenvalues. An appeal of this result stems from the fact that the mplet of internal points must be assumed rational. Otherwise, the estimate is shown to cease to be valid. The author also outlines a few further improvements of his/her estimate in the rational cases.  
Remarks to the editors:  