Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms

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• 作者：Chiara Boiti^a ; ^{chiara.boiti@unife.it" class="auth_mail" title="E-mail the corresponding author} ; David Jornet^b ; ^{djornet@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Alessandro Oliaro^c ; ^{alessandro.oliaro@unito.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Regularity ; Linear partial differential operators with polynomial coefficients ; Schwartz spaces ; Wigner transform
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：920-944
• 全文大小：505 K

文摘

We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305327&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305327&_rdoc=1&_issn=0022247X&md5=70c5e3447e05a6988e4b1053b4afbc8f" title="Click to view the MathML source">Sclass="mathContainer hidden">class="mathCode">$\mathcal{S}$ and in the space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305327&_mathId=si15.gif&_user=111111111&_pii=S0022247X16305327&_rdoc=1&_issn=0022247X&md5=78970509751aee57e7ee15b0b462b310" title="Click to view the MathML source">S_ωclass="mathContainer hidden">class="mathCode">${\mathcal{S}}_{\omega }$ as introduced by Björck for weight functions ω. Several examples are discussed in this new setting.