ON THE BOUNDEDNESS OF THE L-INDEX IN DIRECTION OF ENTIRE SOLUTIONS OF THE GOLDBERG-STRELITZ EQUATION
DOI:
https://doi.org/10.31471/2304-7399-2025-20(76)-9-14Keywords:
entire solution, bounded index in direction, linear first-order partial differential equation.Abstract
For some linear first-order partial differential equation there is proved the boundedness of the $L$-index in the direction $\mathbf{b}=(b_1,b_2)$ of all its entire bivariate solutions with bounded multiplicity of zero points. The function $L$ is defined as the modulus of the product of the derivative in the direction $\mathbf{b}$ of the function $zw$ on the function $l(zw)$, and an entire solution is represented by the product of the exponential function $e^z$ and an arbitrary entire function $f(zw)$ such that $f: \mathbb{C}\to\mathbb{C}$ has bounded $l$-index.References
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