algebraic microlocalization in nLab

Contents

Idea

As an analogue of the microlocalization in operator theory, T. Springer has introduced an algebraic microlocalization in the theory of filtered noncommutative rings.

Microlocal analysis using hyperfunctions instead of Schwartz distributions is also called algebraic microlocal analysis.

References

An alternative way to algebraic microlocalization is given in

• Maria J. Asensio, Michel Van den Bergh, Freddy Van Oystaeyen, A new algebraic approach to microlocalization of filtered rings, Trans. Amer. Math. Soc. 316, 2 (Dec. 1989) 537–553 jstor

This is used in comparison to Kapranov’s noncommutative geometry based on commutator expansion in

• Lieven Le Bruyn, Formal structures and representation spaces, J. Algebra 247, 616–635 (2002) doi

An introduction to the microlocal analysis of hyperfunctions is this:

• Goro Kato, Daniele C. Struppa: Fundamentals of algebraic microlocal analysis (ZMATH entry)