Spectral calculations in rings

Details Spectral calculations in rings Spectral calculations in rings

2006-10-30

arxiv.org/abs/math/0610921v3

Annales Univ. Sci. Budapest, 54 (2011), pp. 7-34

Mathematics

Rings and Algebras

16 pages

Scientific paper

We examine the validity of certain spectral integral formulas in topological rings. We consider the sign and square-root functions in polymetric rings containing $\frac12$. It turns out that formal analogues of classical transformation kernels and the resolvent identity can be used to understand the situation. In the lack of $\frac12$, the functions $\frac12-\frac12\sgn(\frac12-z)$ and $\frac12-\sqrt{\frac14-z}$ can be generalized, respectively.

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