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Singular points of the Hadamard composition
Let \(f(z)\), \(g(z)\) be power series \(f(z)=\sum_{n\geq 0}f_ nz^ n\), \(g(z)=\sum_{n\geq 0}g_ nz^ n\), let \(r_ f\), \(r_ g\) be their radii of convergence, and let \[ h(z)=\sum_{n\geq 0}h_ nz^ n \] be their Hadamard composition. Then \(r_ h\geq r_ fr_ g\). The authors prove the following. Theorem. Let \(r_ h=r_ f=r_ g=1\). If (a) the function \(f(z)\
Yu F Korobeinik, Korobeinik Yu F
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Multidimensional Hadamard composition and sums with linear constraints on the summation indices
Siberian Mathematical Journal, 1989Let D be an (m\(\times n)\)-dimensional matrix with integer entries and let \(\mu \in {\mathbb{Z}}^ n\). Given two power series \(f(\xi)=\sum a(\alpha)\xi^{\alpha}\), \((\xi \in {\mathbb{C}}^ n\), \(\alpha \in ({\mathbb{Z}}_+)^ n)\) and \(g(\eta)=\sum b(\beta)\eta^{\beta}\) \((\eta \in {\mathbb{C}}^ m\), \(\beta \in ({\mathbb{Z}}_+)^ m)\) the author ...
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Hadamard matrices of composite orders
2022Summary: In this paper, we give a method for the constructions of Hadamard matrices of composite orders by using suitable \(T\)-matrices and known Hadamard matrices. We establish a formula for \(T\)-matrices and Hadamard matrices and discuss under what condition we can get \(T\)-matrices from the known Hadamard matrices.
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On Hadamard Compositions of Gelfond–Leontiev Derivatives of Analytic Functions
Russian Mathematics, 2020For analytic functions f and g, the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders. A relation between the behaviors of the maximal terms of the Hadamard composition of Gelfond-Leont'ev derivatives and those of the Gelfond-Leont'ev derivative of a Hadamard composition is ...
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