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Moebius transformations and monogenic functional calculus
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## Moebius transformations and

monogenic functional calculus

### Vladimir V. Kisil

**Abstract.**
A new way of doing functional calculi is presented. A
functional calculus $\Phi: f(x)\rightarrow f(T)$ is not an algebra
homomorphism of a functional algebra into an operator algebra, but
an intertwining operator between two representations of a group
acting on two mentioned algebras (as linear spaces).
This scheme is shown on the newly developed monogenic functional
calculus for an arbitrary set of non-commuting self-adjoint
operators. The corresponding spectrum and spectral mapping
theorem are included.

*Copyright American Mathematical Society 1996*

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#### Article Info

- ERA Amer. Math. Soc.
**02** (1996), pp. 26-33
- Publisher Identifier: S 1079-6762(96)00004-7
- 1991
*Mathematics Subject Classification*. Primary 46H30, 47A13;
Secondary 30G35, 47A10, 47A60, 47B15, 81Q10
- Received by the editors October 6, 1995, and, in revised form,
March 9, 1996
- Communicated by Alexandre Kirillov
- Comments (When Available)

**Vladimir V. Kisil**

Institute of Mathematics Economics and Mechanics,
Odessa State University,
ul. Petra Velikogo, 2,
Odessa-57, 270057, UKRAINE

*E-mail address:* `vk@imem.odessa.ua`

This work was partially supported by the INTAS grant 93-0322.
It was finished while the author enjoyed the hospitality of
Universiteit Gent, Vakgroep Wiskundige Analyse, Belgium.

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