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«ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա»-ն լույս է տեսնում 1966 թվականից՝ տարին 6 անգամ։
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Գլխավոր խմբ․՝ Մ․ Մ․ Ջրբաշյան (1966-1994) ; Ռ․ Վ․ Համբարձումյան (1994-2009) ; Ա․ Ա․ Սահակյան (2010-)
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Turning point ; Sturm-Liouville problem ; nondefinite problem ; infinite products ; Hadamard factorization ; spectral theory.
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The paper studies the differential equation yn + (р2ф2(х ) - q(x)) y = 0 (*) on the interval I = [0, 1], containing a finite number of zeros 0 < x1 < X2 < ... < < xm < 1 of ф2 , i.e. so-called turning points. Using asymptotic estimates from [6] for appropriate fundamental systems of solutions of (*) as \p\ →∞ < x, it is proved that, if there is an asymptotic solution of the initial value problem generated by (*) in the interval [0,x1 ) , then the asymptotic solutions in the remaining intervals can be obtained recursively. Furthermore, an infinite product representation of solutions of ( * ) is studied. The representations are useful in the study of inverse spectral problems for such equations.
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Երևան
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ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան