{'fraction_non_alphanumeric': 0.015985790408525755, 'fraction_numerical': 0.007104795737122558, 'mean_word_length': 5.130434782608695, '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}}
Time-Frequency Localizations for Modulation Spaces on Locally Compact Abelian Groups

In the present paper we define weighted modulation spaces on a LCA group with respect to a window function drawn from a suitable Banach space of test functions and prove a theorem to establish uncertainty principle for these modulation spaces. Also, using the concept of Zak transform, we generalize an earlier result of Heil (1990) on the Balian–Low theorem for the Wiener amalgam space . Our theorems include the corresponding results on Euclidean spaces as particular cases.