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

2024/06/21 by Subhankar Mahapatra, Mahapatra, Subhankar, Santanu Sarkar +1
Mathematics · #47A56 #47A68 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary: 46E22 #Secondary: 30D10

paper · pdf · doi:10.48550/arxiv.2406.15194

openalex publication_date 2024/06/21 · openalex created_date 2024/06/25 · openalex updated_date 2026/07/28

Abstract

This paper extends the concept of de Branges matrices to any finite m× m order where m=2n. We shall discuss these matrices along with the theory of de Branges spaces of ℂⁿ-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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