{'fraction_non_alphanumeric': 0.012152777777777778, 'fraction_numerical': 0.0, 'mean_word_length': 5.138297872340425, '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}}
Conditional stability for a Cauchy problem for the ultrahyperbolic Schrödinger equation

ABSTRACT In this work, we first establish a local Carleman estimate for the ultrahyperbolic Schrödinger equation which arises in some theories of modern physics such as quantum mechanics and string theory. Next, we prove a Hölder stability estimate for the Cauchy Problem. In the proof, we introduce a suitable cut-off function and extend Cauchy data in a Sobolev space to reduce the problem to another problem for functions with compact supports and then we apply the Carleman estimate.