New findings on the Bank-Sauer approach in oscillation theory

DOI10.1007/s00365-011-9137-8zbMath1256.34080OpenAlexW1996239400MaRDI QIDQ431159

Janne Gröhn, Janne Heittokangas

Publication date: 26 June 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-011-9137-8

zbMATH Keywords

oscillation theoryBlaschke productlogarithmic derivativeBlaschke-oscillatoryinterploationKorenblum's spaceprescribed zero sequenceuniformly separated sequence

Mathematics Subject Classification ID

Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10) Linear ordinary differential equations and systems in the complex domain (34M03) Blaschke products (30J10)

Related Items (13)

Fixed points and solutions of boundary value problems at resonance ⋮ ON THE COMPLEXITY OF FINDING A NECESSARY AND SUFFICIENT CONDITION FOR BLASCHKE-OSCILLATORY EQUATIONS ⋮ On non-normal solutions of linear differential equations ⋮ Multiple interpolation with the fast-growing knots in the class of entire functions and its application ⋮ Zero separation results for solutions of second order linear differential equations ⋮ Solutions of complex differential equation having pre-given zeros in the unit disc ⋮ Solutions of second order complex differential equation having certain pre-given zeros ⋮ Deficient values of solutions of linear differential equations ⋮ Converse growth estimates for ODEs with slowly growing solutions ⋮ On interpolation problem with derivative in the space of entire functions with fast-growing interpolation knots ⋮ On non-separated zero sequences of solutions of a linear differential equation ⋮ Interpolation of analytic functions of moderate growth in the unit disc and zeros of solutions of a linear differential equation ⋮ A Survey on Blaschke-Oscillatory Differential Equations, with Updates

Cites Work

• Properties of meromorphic \(\varphi \)-normal functions
• On interpolating Blaschke products and Blaschke-oscillatory equations
• Solutions of \(f+A (z) f=0\) in the unit disc having Blaschke sequences as the zeros
• A note on the zero-sequences of solutions of linear differential equations
• An extension of the Nevanlinna theory
• Factorization theorems for functions in the Bergman spaces
• Blaschke-oscillatory equations of the form \(f+A(z)f=0\)
• Growth estimates for logarithmic derivatives of Blaschke products and of functions in the Nevanlinna class
• A note on the zero-sequences of solutions of 𝑓”+𝐴𝑓=0
• Complex Nonoscillation Theorems and Criteria of Univalence
• Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates
• On the mean growth of the solutions of complex linear differential equations in the disk
• [https://portal.mardi4nfdi.de/wiki/Publication:4740850 On the Oscillation Theory of f � � + Af = 0 where A is Entire]
• An $L^p$ definition of interpolating Blaschke products
• Blaschke Quotients and Normality
• Some Lemmas on Interpolating Blaschke Products and a Correction
• Zeros of the hypergeometric polynomials \(F(-n,b;2b;z)\)
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