منابع مشابه
Sturm Oscillation and Comparison Theorems
This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.
متن کاملThe Theorems of Oscillation of Sturm
complementary with respect to n of the given combination. Suppose now we form the nm combinations of any n numbers m at a time and consider the set of combinations formed by combining each of these nm combinations with their complementaries in such a way that the numbers in any combination arranged in their natural order are immediately followed by the numbers in the complementary combination a...
متن کاملOn Oscillation Theorems for Differential Polynomials
In this paper, we investigate the relationship between small functions and differential polynomials gf (z) = d2f ′′ + d1f ′ + d0f , where d0 (z) , d1 (z) , d2 (z) are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation f ′′ + Af ′ +Bf = F, where A, B, F 6≡ 0 are finite order meromorphic functions having o...
متن کاملSome Theorems of Comparison and Oscillation
+ S&iX2(Xi — X2)} = 0. Clearly, the quartic degenerates into the #-line of the pencil of cubics, and into a cubic having (si, s2) sz) as the $-point. Hence the THEOREM: Any cubic of the net with a given S-point may be generated by any pencil of cubics within the net, not containing the given cubic, and the projective pencil of lines joining the Spoint of the given cubic to the S-points of the c...
متن کاملOscillation Theorems for Symplectic Difference Systems
We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same pr...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1948
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1948-0027925-7