Recent zbMATH articles in MSC 30D20https://www.zbmath.org/atom/cc/30D202022-05-16T20:40:13.078697ZWerkzeugThe fundamental theorem of algebra and Liouville's theorem geometrically revisitedhttps://www.zbmath.org/1483.300272022-05-16T20:40:13.078697Z"Almira, Jose Maria"https://www.zbmath.org/authors/?q=ai:almira.jose-maria"Romero, Alfonso"https://www.zbmath.org/authors/?q=ai:romero.alfonsoSummary: If \(f(z)\) is either a polynomial with no zeroes or a bounded entire function, then a Riemannian metric \(g_f\) is constructed on the complex plane \(\mathbb{C}\). This metric \(g_f\) is shown to be flat and geodesically complete. Therefore, the Riemannian manifold \((\mathbb{C}, g_f)\) must be isometric to \((\mathbb{C}, |dz|^2)\), which implies that \(f(z)\) is a constant.Uniqueness of differential \(q\)-shift difference polynomials of entire functionshttps://www.zbmath.org/1483.300622022-05-16T20:40:13.078697Z"Mathai, Madhura M."https://www.zbmath.org/authors/?q=ai:mathai.madhura-m"Manjalapur, Vinayak V."https://www.zbmath.org/authors/?q=ai:manjalapur.vinayak-vSummary: In this paper, we prove the uniqueness theorems of differential \(q\)-shift difference polynomials of transcendental entire functions.On conditions of the completeness of some systems of Bessel functions in the space \(L^2 ((0;1); x^{2p} dx)\)https://www.zbmath.org/1483.420232022-05-16T20:40:13.078697Z"Khats, R. V."https://www.zbmath.org/authors/?q=ai:khats.r-vIn this paper the author gives necessary and sufficient conditions for the system \(\{x^{-p-1}\sqrt{x\rho_k}J_\nu(x\rho_k): k \in \mathbb{N}\}\) to be complete in the weighted space \(L^2((0,1), x^{2p} dx)\). Here \(J_\nu\) is the first kind Bessel function of index \(\nu \geq \frac{1}{2}\), \(p \in \mathbb{R}\) and \(\rho_k : k \in \mathbb{N}\) is an arbitrary sequence of distinct nonzero complex numbers.
The fact that \(\rho_k\) can be arbitrary had already been considered by \textit{B. V. Vynnyts'kyi} and \textit{R. V. Khats'} [Eurasian Math. J. 6, No. 1, 123--131 (2015; Zbl 1463.30015)]. In the present paper, he gives new conditions which depend only on properties of the \(\rho_k\).
Reviewer: Ursula Molter (Buenos Aires)