All reports by Author Günter Hotz:

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TR04-006
| 6th January 2004
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Günter Hotz#### A remark on nondecidabilities of the initial value problem of ODEs

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TR01-004
| 13th October 2000
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Tobias Gärtner, Günter Hotz#### Recursive analytic functions of a complex variable

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TR95-025
| 8th May 1995
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Günter Hotz, Gero Vierke, Bjoern Schieffer#### Analytic Machines

Comments: 1

Günter Hotz

We prove that it is not decidable on R-machines if for a fixed finite intervall [a,b) the solution of the initial value problems of systems of ordinary differetial equations have solutions over this interval. This result holds independly from assumptions about differentiability of the right sides of the ODEs. Futhermore ... more >>>

Tobias Gärtner, Günter Hotz

We extend the concept of recursive definition on analytic functions. For special cases of linear primitive recursive definitions we show the existence of natural continuations of the over $\N$ primitive recursive functions to analytic functions. Especially, we show that solutions exist if the coefficients of the linear recursive equation are ... more >>>

Günter Hotz, Gero Vierke, Bjoern Schieffer

In this paper the $R$-machines defined by Blum, Shub and Smale

are generalized by allowing infinite convergent computations.

The description of real numbers is infinite.

Therefore, considering arithmetic operations on real numbers should

also imply infinite computations on {\em analytic machines}.

We prove that $\R$-computable functions are $\Q$-analytic.

We show ...
more >>>