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Alex M.
Alex M.
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Are there characterizations of Schwartz regular distributions other than being locally integrable (which does not lend itself to easy manipulations)?

To be more detailed: if I want to show that some distribution is in fact a smooth function, I can try to use the concepts of singular support or wavefront, together with hypoellipticity. What can I do if I want much less, namely to show that a distribution is only a locally-integrable function (not necessarily smooth)?

Are there characterizations of Schwartz regular distributions other than being locally integrable (which does lend itself to easy manipulations)?

To be more detailed: if I want to show that some distribution is in fact a smooth function, I can try to use the concepts of singular support or wavefront, together with hypoellipticity. What can I do if I want much less, namely to show that a distribution is only a locally-integrable function (not necessarily smooth)?

Are there characterizations of Schwartz regular distributions other than being locally integrable (which does not lend itself to easy manipulations)?

To be more detailed: if I want to show that some distribution is in fact a smooth function, I can try to use the concepts of singular support or wavefront, together with hypoellipticity. What can I do if I want much less, namely to show that a distribution is only a locally-integrable function (not necessarily smooth)?

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Alex M.
Alex M.
  • 5.4k
  • 11
  • 35
  • 52

Recognizing Schwartz regular distributions

Are there characterizations of Schwartz regular distributions other than being locally integrable (which does lend itself to easy manipulations)?

To be more detailed: if I want to show that some distribution is in fact a smooth function, I can try to use the concepts of singular support or wavefront, together with hypoellipticity. What can I do if I want much less, namely to show that a distribution is only a locally-integrable function (not necessarily smooth)?