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Spectral resolutions for non-self-adjoint block convolution operators

Zalot Ewelina

Opuscula Mathematica

2022

Vol. 42, no. 3

459--487

The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.

Spectral representations for a class of banded Jacobi-type matrices

Zalot E., Majdak W.

Opuscula Mathematica

2014

Vol. 34, no. 4

871--887

We describe some spectral representations for a class of non-self-adjoint banded Jacobi-type matrices. Our results extend those obtained by P.B. Naïman for (two-sided infinite) periodic tridiagonal Jacobi matrices.