Global M-Hypoellipticity, Global M-Solvability and Perturbations by Lower Order Ultradifferential Pseudodifferential Operators

Autor(es)

Ferra, Igor Ambo ^[1] ; Petronilho, Gerson ^[2] ; Victor, Bruno de Lessa ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Alameda Univ S-N, BR-09606045 Sao Bernardo Do Campo, SP - Brazil

^[2] Univ Fed Sao Carlos UFSCar, Dept Matemat, BR-13569905 Sao Carlos, SP - Brazil

^[3] Univ Fed Parana, Dept Matemat, BR-82590300 Curitiba, Parana - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS; v. 26, n. 6 DEC 2020.
• Citações Web of Science: 0

Resumo

We introduce a new class of ultradifferentiable pseudodifferential operators on the toruswhose calculus allows us to showthat global hypoellipticity, in ultradifferentiable classes, with a finite loss of derivatives of a system of pseudodifferential operators, is stable under perturbations by lower order pseudodifferential operators whose order depends on the loss of derivatives. The key point in our study is our definition of loss of derivatives. We also give an easy proof of the fact that if a system of pseudodifferential operators is globallyM-hypoelliptic then its transpose is globally solvable in D'(M) (T-N). Finally we present an application of our results. (AU)

• Processo FAPESP: 18/14316-3 - Teoria geométrica de EDP e análise complexa multidimensional
• Beneficiário: Paulo Domingos Cordaro
• Modalidade de apoio: Auxílio à Pesquisa - Temático