2015/10/06 by František Štampach, Stampach, F., P. Šťovı́ček +1
Computer Science · Mathematics · #11A55 #33C99 #47B36 #Advanced Combinatorial Mathematics #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1510.01454
openalex publication_date 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associated, called the characteristic function, whose zero set coincides with the point spectrum of the corresponding Jacobi operator. Here it is shown that the characteristic function admits Hadamard's factorization in two possible ways -- either in the spectral parameter or in an auxiliary parameter which may be called the coupling constant. As an intermediate result, an explicit expression for the power series expansion of the logarithm of the characteristic function is obtained.