{'fraction_non_alphanumeric': 0.03171953255425709, 'fraction_numerical': 0.005008347245409015, 'mean_word_length': 4.9405940594059405, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Generalized Chebyshev polynomials and discrete Schrödinger operators

We investigate a solution of the difference equation with the boundary conditions U0A,B = I, U-1A,B = 0, where A, B are Hermitian elements of a C*-algebra. UnA,B are usually called generalized Chebyshev polynomials of the second kind. The equation () cannot be easily simplified as in the scalar case because A and B do not need to commute. However, we are able to compute the spectrum of the corresponding orthogonality measure which is very important for the investigation of the discrete Schrodinger operator related to UnA,B.