caa a22 4500 475839072 CHVBK 20180406123856.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1023/A:1006413306541 doi (NATIONALLICENCE)springer-10.1023/A:1006413306541 Van Iseghem Jeannette Laboratoire d"Analyse Numerique et d"Optimisation, USTL, 59655, Villeneuve d"Ascq Cedex, France. e-mail aut Matrix Continued Fraction for the Resolvent Function of the Band Operator [Elektronische Daten] [Jeannette Van Iseghem] The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q − 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered. Kluwer Academic Publishers, 2000 genetic sums nationallicence Stieltjes functions nationallicence nonsymmetric difference operators nationallicence vector and matrix orthogonality nationallicence Hermite-Padé approximation nationallicence vector and matrix continued fraction nationallicence direct and inverse spectral problem nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 351-365 0167-8019 61:1-3<351 2000 61 10440 https://doi.org/10.1023/A:1006413306541 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006413306541 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Van Iseghem Jeannette Laboratoire d"Analyse Numerique et d"Optimisation, USTL, 59655, Villeneuve d"Ascq Cedex, France. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 61/1-3(2000-05-01), 351-365 0167-8019 61:1-3<351 2000 61 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer