Asymptotics of pseudodifferential operators acting on functions with corner singularities

Abstract

A new definition of the expansion in smoothness of a distribution at a point is introduced. Some properties of the new expansion are studied and a uniqueness result for the coefficients of the expansion is proved. The main application of the definition is for obtaining the asymptotics in smooth ness of pseudodifferential operators acting on a function near a corner point of singsupp f. An example of usage of the obtained results in computed tomog raphy is presented.

Keywords:

• Distributions
• expansion in smoothness
• pseudodifferential operators
• corners
• computed tomography

AMS:

• 41A60
• 46F12
• 47G30
• 65R10
• 44A12
• 92C55