scholarly journals Global hypoellipticity and simultaneous approximability in ultradifferentiable classes

2017 ◽  
Vol 453 (1) ◽  
pp. 104-124 ◽  
Author(s):  
R.F. Barostichi ◽  
I.A. Ferra ◽  
G. Petronilho
Keyword(s):  
Global Hypoellipticity

scholarly journals Propagation of regularity and global hypoellipticity

2002 ◽  
Vol 50 (3) ◽  
pp. 471-482 ◽  
Author(s):  
A. Alexandrou Himonas ◽  
Gerson Pentronilho
Keyword(s):  
Global Hypoellipticity

scholarly journals Global Hypoellipticity and Simultaneous Approximability

2000 ◽  
Vol 170 (2) ◽  
pp. 356-365 ◽  
Author(s):  
A.Alexandrou Himonas ◽  
Gerson Petronilho
Keyword(s):  
Global Hypoellipticity

scholarly journals PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA

2002 ◽  
Vol 45 (3) ◽  
pp. 731-759 ◽  
Author(s):  
Detta Dickinson ◽  
Todor Gramchev ◽  
Masafumi Yoshino
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Pseudodifferential Operators ◽  
Zeroth Order ◽  
Gevrey Regularity ◽  
Exceptional Sets ◽  
Secondary 58J40 ◽  
Elliptic Pseudodifferential Operator ◽  
Primary 37C15 ◽  
Global Hypoellipticity

AbstractThis paper concerns perturbations of smooth vector fields on $\mathbb{T}^n$ (constant if $n\geq3$) with zeroth-order $C^\infty$ and Gevrey $G^\sigma$, $\sigma\geq1$, pseudodifferential operators. Simultaneous resonance is introduced and simultaneous resonant normal forms are exhibited (via conjugation with an elliptic pseudodifferential operator) under optimal simultaneous Diophantine conditions outside the resonances. In the $C^\infty$ category the results are complete, while in the Gevrey category the effect of the loss of the Gevrey regularity of the conjugating operators due to Diophantine conditions is encountered. The normal forms are used to study global hypoellipticity in $C^\infty$ and Gevrey $G^\sigma$. Finally, the exceptional sets associated with the simultaneous Diophantine conditions are studied. A generalized Hausdorff dimension is used to give precise estimates of the ‘size’ of different exceptional sets, including some inhomogeneous examples.AMS 2000 Mathematics subject classification: Primary 37C15; 11J13. Secondary 58J40; 11J20; 35H05

scholarly journals Global hypoellipticity for strongly invariant operators

2020 ◽  
Vol 486 (1) ◽  
pp. 123878 ◽  
Author(s):  
Alexandre Kirilov ◽  
Wagner A.A. de Moraes
Keyword(s):  
Global Hypoellipticity
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