Global hypoellipticity for a class of periodic Cauchy operators

被引:2
|
作者
Silva, Fernando de Avila [1 ]
机构
[1] Univ Fed Parana, Dept Math, Caiza Postal 19081, BR-81531980 Curitiba, Parana, Brazil
关键词
Global hypoellipticity; Pseudo-differential operators; Fourier series; Cauchy operators; Siegel conditions; VECTOR-FIELDS; SOLVABILITY; TORUS;
D O I
10.1016/j.jmaa.2019.123650
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This note presents an investigation on the global hypoellipticity problem for Cauchy operators on Tn+1 belonging to the class L = Pi(m)(j=1) (D-t + c(j)(t)P-j(D-x)), where Pj(D-x) are pseudo-differential operators on T-n and c(j)(t) are smooth complex valued functions on T. The main goal of this investigation consists in establishing connections between the global hypoellipticity of the operators L and its normal form L-0 = Pi(m)(j=1) (D-t + c(0,j)P(j)(D-x)). In order to do so, the problem is approached by combining Hormander's and Siegel's conditions on the symbols of the operators Lj = D-t + c(j)(t)P-j(D-x). (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页数:10
相关论文
共 50 条
  • [1] Global hypoellipticity and global solvability for a class of operators on compact manifolds
    Bergamasco, AP
    Caetano, PAS
    Kondo, CI
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 141 (02) : 236 - 253
  • [2] Hypoellipticity and well-posedness of the Cauchy problem for a class of degenerate elliptic operators
    Mughetti, M
    [J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2001, 4A (03): : 511 - 514
  • [3] Global Hypoellipticity for a Class of Pseudo-differential Operators on the Torus
    Fernando de Ávila Silva
    Rafael Borro Gonzalez
    Alexandre Kirilov
    Cleber de Medeira
    [J]. Journal of Fourier Analysis and Applications, 2019, 25 : 1717 - 1758
  • [4] GLOBAL ANALYTIC HYPOELLIPTICITY OF A CLASS OF DEGENERATE ELLIPTIC OPERATORS ON THE TORUS
    Cordaro, Paulo D.
    Himonas, A. Alexandrou
    [J]. MATHEMATICAL RESEARCH LETTERS, 1994, 1 (04) : 501 - 510
  • [5] ON THE HYPOELLIPTICITY OF DIFFERENTIAL-OPERATORS IN THE CLASS OF GENERALIZED PERIODIC-FUNCTIONS
    POPIVANOV, PR
    [J]. DOKLADY AKADEMII NAUK SSSR, 1982, 266 (03): : 565 - 568
  • [6] GLOBAL HYPOELLIPTICITY OF A CLASS OF 2ND-ORDER OPERATORS
    BERGAMASCO, AP
    ZANI, SL
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1994, 37 (03): : 301 - 305
  • [8] Global Hypoellipticity for a Class of Pseudo-differential Operators on the Torus
    Silva, Fernando de Avila
    Gonzalez, Rafael Borro
    Kirilov, Alexandre
    de Medeira, Cleber
    [J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2019, 25 (04) : 1717 - 1758
  • [9] Hypoellipticity for a class of operators with multiple characteristics
    Marco Mughetti
    Fabio Nicola
    [J]. Journal d'Analyse Mathématique, 2007, 103 : 377 - 396
  • [10] Hypoellipticity for a class of operators with multiple characteristics
    Mughetti, Marco
    Nicola, Fabio
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2007, 103 (1): : 377 - 396