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arXiv · 2406.15194

de Branges matrices and associated de Branges spaces of vector valued entire functions

Subhankar Mahapatra·Santanu Sarkar
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Abstract

This paper extends the concept of de Branges matrices to any finite $m\times m$ order where $m=2n$. We shall discuss these matrices along with the theory of de Branges spaces of $\mathbb{C}^n$-valued entire functions and their associated functions. A parametrization of these matrices is obtained using the Smirnov maximum principle for matrix valued functions. Additionally, a factorization of matrix valued meromorphic functions is discussed.

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Subhankar Mahapatra, Santanu Sarkar. 2024-06-21. de Branges matrices and associated de Branges spaces of vector valued entire functions. https://arxiv.org/abs/2406.15194

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