{'fraction_non_alphanumeric': 0.02541544477028348, 'fraction_numerical': 0.0039100684261974585, 'mean_word_length': 5.2439024390243905, '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}}
Recent representation results for linear system maps: A short survey

We give an expression for the most general input–output map associated with the members of a certain important large family of multidimensional linear shift‐invariant systems with bounded Lebesgue‐measurable inputs. The expression given is an iterated function‐space limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution with an integrable impulse–response function. A key role is played by a certain family of weighting operators. It is observed that for the large family of inputs and maps addressed, the Dirac impulse–response concept is in fact not the key concept concerning the representation of H, and that instead the input–output properties of H are determined, in general, by a certain type of family of responses. Some related material concerning other results, engineering education, and discrete‐space systems, is also given. Copyright © 2007 John Wiley & Sons, Ltd.