Right Semidefinite Eigenvalue Problems

Binding, Paul; Volkmer, Hans

doi:10.1017/s0013091502000603

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Existence Of Eigenvalues1

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Cited by 3 publications

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“…For example, the quantities − J are related to zero counts in the following way. If Under the additional assumption that s(x) > 0 a.e., Corollary 5.6 was proved first by Everitt, Kwong and Zettl [6] and then in an operator theoretic setting by Binding and Browne [3]; see also [5]. It is interesting to note that the proofs in [3], [6] and the one given in this section are all quite different.…”

Section: Existence Of Eigenvaluesmentioning

confidence: 81%

Prüfer angle asymptotics for Atkinson's semi‐definite Sturm–Liouville eigenvalue problem

Binding¹,

Volkmer

2005

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Key words Sturm-Liouville problem, Prüfer angle, asymptotics of eigenvalues MSC (2000) 34L20To the memory of a friend who still teaches us so much Atkinson's semi-definite Sturm-Liouville problem consists of the differential equation −(y /s) + qy = λry, with s, q, r integrable on [a, b], q real-valued, s, r ≥ 0, and separated boundary conditions at a, b. The asymptotic behavior of the associated Prüfer angle is determined as λ → ±∞. This leads to existence theorems for eigenvalues λn with prescribed oscillation number n and their asymptotics. In general, λn grows faster than n 2 , and the order of the corresponding characteristic function is less than 1 2 .

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