Open AccessOn the boundary conditions for products of Sturm-Liouville differential operators
Author(s) -
Sobhy El-Sayed Ibrahim
Publication year - 2001
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.32.2001.374
Subject(s) - sturm–liouville theory , mathematics , characterization (materials science) , domain (mathematical analysis) , order (exchange) , product (mathematics) , pure mathematics , differential operator , interval (graph theory) , differential (mechanical device) , mathematical analysis , extension (predicate logic) , boundary (topology) , boundary value problem , combinatorics , physics , geometry , computer science , finance , optics , economics , thermodynamics , programming language
In this paper, the second-order symmetric Sturm-Liouville differential expressions $ au_1, au_2, ldots, au_n $ with real coefficients are considered on the interval $ I = (a,b) $, $ - infty le a < b le infty $. It is shown that the characterization of singular self-adjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximan domain of the product operators, and is an exact parallel of the regular case. This characterization is an extension of those obtained in [6], [8], [11-12], [14] and [15].