J. Heittokangas

activity

20192024

most citedDual exponential polynomials and a problem of Ozawa

3 citations · 10 across the 19 of their papers we have counts for

collaborators

20 papers

math.CA2024

Convergence of sub-series' and sub-signed series' in terms of the asymptotic $ψ$ -density

Janne Heittokangas, Zinelaabidine Latreuch

Given a non-negative real sequence ${c_{n}}_{n}$ such that the series $\sum_{n = 1}^{\infty} c_{n}$ diverges, it is known that the size of an infinite subset $A \subset N$ can be m…

math.CA2024

Asymptotic $ψ$ -densities of subsets of natural numbers

Janne Heittokangas, Zinelaabidine Latreuch

The sizes of subsets of the natural numbers are typically quantified in terms of asymptotic (linear) and logarithmic densities. These concepts have been generalized to weighted $w$ …

math.CV2023

Standard solutions of complex differential equations

Janne Heittokangas, Samu Pulkkinen, Hui Yu +1

A meromorphic solution of a complex linear differential equation (with meromorphic coefficients) for which the value zero is the only possible finite deficient/deviated value is ca…

math.CV2022

Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory

Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge +1

An exponential polynomial is a finite linear sum of terms $P (z) e^{Q (z)}$ , where $P (z)$ and $Q (z)$ are polynomials. The early results on the value distribution of exponential polyno…

math.CV2021★ 3 cited

Dual exponential polynomials and a problem of Ozawa

Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge +1

Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of a…

math.CV2021

Meromorphic functions of finite $φ$ -order and linear Askey-Wilson divided difference equations

Hui Yu, Janne Heittokangas, Jun Wang +1

The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The $φ$ -order is used as a general growth indi…

math.CA2020★ 2 cited

Irregular finite order solutions of complex LDE's in unit disc

Igor Chyzhykov, Petro Filevych, Janne Gröhn +2

It is shown that the order and the lower order of growth are equal for all non-trivial solutions of $f^{(k)} + A f = 0$ if and only if the coefficient $A$ is analytic in the unit disc…

math.CV2020

Meromorphic functions of finite $φ$ -order and linear $q$ -difference equations

Janne Heittokangas, Jun Wang, Zhi-Tao Wen +1

The $φ$ -order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, t…

math.CV2020

Asymptotic integration theory for $f^{''} + P (z) f = 0$

Gary G. Gundersen, Janne Heittokangas, Amine Zemirni

Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) $f^{''} + P (z) f = 0$ ,…

math.CV2020

On Petrenko's deviations and second order differential equations

J. Heittokangas, M. A. Zemirni

New results on the oscillation of solutions of $f^{''} + A (z) f = 0$ and on the growth of solutions of $f^{''} + A (z) f^{'} + B (z) f = 0$ are obtained, where $A$ and $B$ are entire functions. Petrenko's…

math.CV2019

On meromorphic solutions of non-linear differential equations of Tumura-Clunie type

Janne Heittokangas, Zinelaabidine Latreuch, Jun Wang +1

Meromorphic solutions of non-linear differential equations of the form $f^{n} + P (z, f) = h$ are investigated, where $n \geq 2$ is an integer, $h$ is a meromorphic function, and $P (z, f)$ i…

math.CV2019

On the number of linearly independent rapid solutions to linear differential and linear difference equations

Janne Heittokangas, Hui Yu, M. Amine Zemirni

Assuming that $A_{0}, \dots, A_{n - 1}$ are entire functions and that $p \in {0, \dots, n - 1}$ is the smallest index such that $A_{p}$ is transcendental, then, by a classical theorem of Fr…

math.CV2019

Contour integral solutions of linear differential equations which include a generalization of the Airy integral

Gary G. Gundersen, Janne M. Heittokangas, Zhi-Tao Wen

The Airy integral is a well-known contour integral solution of Airy's equation which has several applications and which has been used for mathematical illustrations due to its inte…

math.CV2019★ 1 cited

A continuous transition from $E$ -sets to $R$ -sets and beyond

Jie Ding, Janne Heittokangas, Zhi-Tao Wen

The well-known $E$ -sets introduced by Hayman in 1960 are collections of Euclidean discs in the complex plane with the following property: The set of angles $θ$ for which…

math.CV2019★ 1 cited

The asymptotic number of zeros of exponential sums in critical strips

J. Heittokangas, Z. -T. Wen

Normalized exponential sums are entire functions of the form $f (z) = 1 + H_{1} e^{w_{1} z} + \dots + H_{n} e^{w_{n} z},$ where $H_1,\ldots, H_n\in\C$ and $0 < w_{1} < \dots < w_{n}$ . It is known that the…

math.CV2019★ 1 cited

Deficient values of solutions of linear differential equations

Gary G. Gundersen, Janne Heittokangas, Zhi-Tao Wen

Differential equations of the form $f^{''} + A (z) f^{'} + B (z) f = 0$ (*) are considered, where $A (z)$ and $B (z) \neq \equiv 0$ are entire functions. The Lindelöf function is used to show t…

math.CV2019

Exponential polynomials in the oscillation theory

Janne Heittokangas, Katsuya Ishizaki, Ilpo Laine +1

Supposing that $A (z)$ is an exponential polynomial of the form $A (z) = H_{0} (z) + H_{1} (z) e^{ζ_{1} z^{n}} + \dots + H_{m} (z) e^{ζ_{m} z^{n}},$ where $H_{j}$ 's are entire and of order $< n$ , it is demons…

math.CV2019★ 1 cited

Generalization of Pólya's zero distribution theory for exponential polynomials, plus sharp results for asymptotic growth

Janne Heittokangas, Zhi-Tao Wen

An exponential polynomial of order $q$ is an entire function of the form $f (z) = P_{1} (z) e^{Q_{1} (z)} + \dots + P_{k} (z) e^{Q_{k} (z)},$ where the coefficients $P_{j} (z), Q_{j} (z)$ are polynomial…

math.CA2019★ 1 cited

Oscillation of solutions of LDE's in domains conformally equivalent to unit disc

Igor Chyzhykov, Janne Gröhn, Janne Heittokangas +1

Oscillation of solutions of $f^{(k)} + a_{k - 2} f^{(k - 2)} + \dots + a_{1} f^{'} + a_{0} f = 0$ is studied in domains conformally equivalent to the unit disc. The results are applied, for e…

math.CA2019

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

Igor Chyzhykov, Janne Gröhn, Janne Heittokangas +1

It is known that, equally well in the unit disc as in the whole complex plane, the growth of the analytic coefficients $A_{0}, \dots, A_{k - 2}$ of \begin{equation*} f^{(k)} + A_{k-2} f…

Convergence of sub-series' and sub-signed series' in terms of the asymptotic ψ-density

Asymptotic ψ-densities of subsets of natural numbers

Standard solutions of complex differential equations

Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory

Dual exponential polynomials and a problem of Ozawa

Meromorphic functions of finite φ-order and linear Askey-Wilson divided difference equations

Irregular finite order solutions of complex LDE's in unit disc

Meromorphic functions of finite φ-order and linear q-difference equations

Asymptotic integration theory for f′′+P(z)f=0

On Petrenko's deviations and second order differential equations

On meromorphic solutions of non-linear differential equations of Tumura-Clunie type

On the number of linearly independent rapid solutions to linear differential and linear difference equations

Contour integral solutions of linear differential equations which include a generalization of the Airy integral

A continuous transition from E-sets to R-sets and beyond

The asymptotic number of zeros of exponential sums in critical strips

Deficient values of solutions of linear differential equations

Exponential polynomials in the oscillation theory

Generalization of Pólya's zero distribution theory for exponential polynomials, plus sharp results for asymptotic growth

Oscillation of solutions of LDE's in domains conformally equivalent to unit disc

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

Convergence of sub-series' and sub-signed series' in terms of the asymptotic $ψ$ -density

Asymptotic $ψ$ -densities of subsets of natural numbers

Meromorphic functions of finite $φ$ -order and linear Askey-Wilson divided difference equations

Meromorphic functions of finite $φ$ -order and linear $q$ -difference equations

Asymptotic integration theory for $f^{''} + P (z) f = 0$

A continuous transition from $E$ -sets to $R$ -sets and beyond