• Corpus ID: 159041370

Description of growth and oscillation of solutions of complex LDE's

@article{Chyzhykov2019DescriptionOG,
  title={Description of growth and oscillation of solutions of complex LDE's},
  author={Igor Chyzhykov and Janne Grohn and Janne Heittokangas and Jouni Rattya},
  journal={arXiv: Classical Analysis and ODEs},
  year={2019}
}
It is known that, equally well in the unit disc as in the whole complex plane, the growth of the analytic coefficients $A_0,\dotsc,A_{k-2}$ of \begin{equation*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0, \quad k\geq 2, \end{equation*} determines, under certain growth restrictions, not only the growth but also the oscillation of its non-trivial solutions, and vice versa. A uniform treatment of this principle is given in the disc $D(0,R)$, $0<R\leq \infty$, by using several… 
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<jats:p>Oscillation of solutions of <jats:inline-formula><jats:alternatives><jats:tex-math>$$f^{(k)} + a_{k-2} f^{(k-2)} + \cdots + a_1 f' +a_0 f = 0$$</jats:tex-math><mml:math

References

SHOWING 1-10 OF 24 REFERENCES
Finiteness of φ-order of solutions of linear differential equations in the unit disc
AbstractIf φ: [0, 1) → (0,∞) is a non-decreasing unbounded function, then the φ-order of a meromorphic function f in the unit disc is defined as $$ \sigma _\phi (f) = \mathop {\lim \sup }\limits_{r
Zero distribution of solutions of complex linear differential equations determines growth of coefficients
It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A0(z), …, Ak−2(z), satisfies λ(f) ⩽ λ ∈ [1, ∞) if and only if the coefficients A0(z), …,
Asymptotic behavior of meromorphic functions of completely regular growth
Suppose X(r) is a positive continuous function on (0, ~) such that X(r) * ~ as r § ~ and is called a growth function. We will assume throughout this paper that X (2r) ~ MK (r) ( ] ) f o r some M > 0
Weighted Bergman spaces induced by rapidly incresing weights
This monograph is devoted to the study of the weighted Bergman space $A^p_\om$ of the unit disc $\D$ that is induced by a radial continuous weight $\om$ satisfying {equation}\label{absteq}
GROWTH ESTIMATES FOR SOLUTIONS OF LINEAR COMPLEX DIFFERENTIAL EQUATIONS
Two methods are used to find growth estimates (in terms of the p-characteristic) for the analytic solutions of f ( k ) + A k - 1 (z)f ( k - 1 ) + ... + A 1 (z)f' + A 0 (z)f = 0 in the disc {z E C:
On the growth of a meromorphic function and its derivatives
The relative rates of growth of a function F meromorphic in the complex plane and its q derivative F (q) are studied via the Nevanlinna Characteristics T(r.F)and T(r.F (q)) and It is shown that lim
ON INTEGRAL FUNCTIONS HAVING PRESCRIBED ASYMPTOTIC GROWTH
where ^(t) is continuous, strictly increasing, and unbounded with ^(1) = 0. This involves no loss of generality since to any function which is increasing and convex in log r and not O(log r) (r —»
Bergman projection induced by radial weight.
The question of when the Bergman projection $P_\omega$ induced by a radial weight $\omega$ on the unit disc is a bounded operator from one space into another is of primordial importance in the theory
Small weighted Bergman spaces
This paper is based on the course \lq\lq Weighted Hardy-Bergman spaces\rq\rq\, I delivered in the Summer School \lq\lq Complex and Harmonic Analysis and Related Topics\rq\rq at the Mekrij\"arvi
FAST GROWING ENTIRE SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS
We investigate the fast growing entire solutions of linear differential equations. For that we introduce a general scale to measure the growth of entire functions of infinite order including
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