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Schwartz, Sur l\u2019impossibilit\u00e9 de la multiplication des distributions, 1954], and such that <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal C_p^{\\infty } \\subseteq \\mathcal A\\subseteq \\mathcal D' $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mi>C<\/mml:mi>\n                      <mml:mi>p<\/mml:mi>\n                      <mml:mi>\u221e<\/mml:mi>\n                    <\/mml:msubsup>\n                    <mml:mo>\u2286<\/mml:mo>\n                    <mml:mi>A<\/mml:mi>\n                    <mml:mo>\u2286<\/mml:mo>\n                    <mml:msup>\n                      <mml:mi>D<\/mml:mi>\n                      <mml:mo>\u2032<\/mml:mo>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal C_p^{\\infty }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msubsup>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mi>p<\/mml:mi>\n                    <mml:mi>\u221e<\/mml:mi>\n                  <\/mml:msubsup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the set of piecewise smooth functions and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal D'$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>D<\/mml:mi>\n                    <mml:mo>\u2032<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the set of Schwartz distributions over <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbb R$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>R<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>). This algebra is endowed with a multiplicative product of distributions, which is a generalization of the product defined in [N.C.Dias, J.N.Prata, A multiplicative product of distributions and a class of ordinary differential equations with distributional coefficients, 2009]. If the algebra is not minimal, but satisfies the previous conditions, is closed under anti-differentiation and the dual product by smooth functions, and the distributional product is continuous at zero then it is necessarily an extension of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal A$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>A<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00605-023-01917-z","type":"journal-article","created":{"date-parts":[[2023,11,4]],"date-time":"2023-11-04T06:02:50Z","timestamp":1699077770000},"page":"43-61","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An existence and uniqueness result about algebras of Schwartz distributions"],"prefix":"10.1007","volume":"203","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9019-8406","authenticated-orcid":false,"given":"Nuno Costa","family":"Dias","sequence":"first","affiliation":[]},{"given":"Cristina","family":"Jorge","sequence":"additional","affiliation":[]},{"given":"Jo\u00e3o Nuno","family":"Prata","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,4]]},"reference":[{"key":"1917_CR1","unstructured":"Ahmad, M. 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