Some Results on the Spectrum of Complex Jacobi Operators

Frantisek Stampach

Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Prague, Czech Republic

We define a function on a subset of the space of all complex sequences and describe its main properties. Next, with the aid of this function, a complex function of one complex variable is constructed. This function is closely related to the spectrum of a certain class of semi-infinite complex Jacobi matrices through its zeros. Results, where the self-adjointness is not to be assumed, are pointed out.

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