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A characterization of holomorphic bivariate functions of bounded index

In: Mathematica Slovaca, vol. 67, no. 3
Richard F. Patterson - Fatih Nuray
Detaily:
Rok, strany: 2017, 731 - 736
Kľúčové slová:
RH-regular, double sequences, Pringsheim limit point, p-convergent, double entire functions
O článku:
The following notion of bounded index for complex entire functions was presented by Lepson. function $f(z)$ is of bounded index if there exists an integer $N$ independent of $z$, such that

$$ \max_{\{l: 0≤ l≤ N\}} \{\frac{\abs{f(l)(z)}}{l!}\} ≥ \frac{\abs{f(n)(z)}}{n!} for all n. $$

The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers $M$ and $N$ such that $M$ and $N$ are the least integers such that

$$\max_{\{(k,l): 0,0≤ k, l≤ M, N\}} \{\frac{\abs{f(k,l)(z,w)}}{k! l!}\} ≥ \frac{\abs{f(m,n)(z,w)}}{m! n!}  for all m and n. $$

Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.
Ako citovať:
ISO 690:
Patterson, R., Nuray, F. 2017. A characterization of holomorphic bivariate functions of bounded index. In Mathematica Slovaca, vol. 67, no.3, pp. 731-736. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0005

APA:
Patterson, R., Nuray, F. (2017). A characterization of holomorphic bivariate functions of bounded index. Mathematica Slovaca, 67(3), 731-736. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0005
O vydaní:
Publikované: 27. 6. 2017