{'fraction_non_alphanumeric': 0.04680365296803653, 'fraction_numerical': 0.010273972602739725, 'mean_word_length': 4.189349112426036, '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}}
On the essential spectra of general differential operators

In this paper, it is shown in the cases of one and two singular endpoints and when all solutions of the equation M[u] - Auw = 0 and its adjoint M + [v] - λwv = 0 are in L 2 w (a, b) (the limit circle case) with f E L 2 w (a,b) for M[u] - λwu = wf that all well-posed extensions of the minimal operator T 0 (M) generated by a general ordinary quasi-differential expression M of nth order with complex coefficients have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression M studied in [1] and [12], and also extend those proved in [8] in the case of one singular end-point of the interval [a, b).