scholarly journals Pseudodifferential operators of infinite order in spaces of tempered ultradistributions

2013 ◽  
Vol 4 (4) ◽  
pp. 495-549 ◽  
Author(s):  
Bojan Prangoski
Keyword(s):  
Infinite Order ◽  
Pseudodifferential Operators ◽  
Tempered Ultradistributions

scholarly journals Local solvability and hypoellipticity for pseudodifferential operators of Egorov type with infinite degeneracy

1995 ◽  
Vol 139 ◽  
pp. 151-171 ◽  
Author(s):  
Yoshinori Morimoto
Keyword(s):  
Pseudodifferential Operator ◽  
Infinite Order ◽  
Pseudodifferential Operators ◽  
Adjoint Operator ◽  
Local Solvability ◽  
Subelliptic Operators ◽  
Subelliptic Operator

Let P be a pseudodifferential operator of the formwhere s, b ≥ 0 are even integers and is odd function with f′(t) > 0 (t ≠ 0). Here . We shall call P an operator of Egorov type because P with f(t) = tk, (k odd) is an important model of subelliptic operators studied by Egorov [1] and Hörmander [3], [4, Chapter 27]. Roughly speaking, any subelliptic operator can be reduced to this operator or Mizohata one after several steps of microlocalization arguments. In this paper we shall study the hypoellipticity of P and the local solvability of adjoint operator P* in the case where f(t) vanishes infinitely at the origin and moreover consider the case where ts and are replaced by functions with zero of infinite order.

Pseudodifferential operators on differential groupoids

1999 ◽  
Vol 189 (1) ◽  
pp. 117-152 ◽  
Author(s):  
Victor Nistor ◽  
Alan Weinstein ◽  
Ping Xu
Keyword(s):  
Pseudodifferential Operators
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