Scan Science and Technology
Contact Leading Edge Experts & Companies
Absolute Convergence
The Experts below are selected from a list of 12780 Experts worldwide ranked by ideXlab platform
Francois Denis – One of the best experts on this subject based on the ideXlab platform.

Absolute Convergence of rational series is semi decidable
Information & Computation, 2011CoAuthors: Raphael Bailly, Francois DenisAbstract:This paper deals with Absolute Convergence of realvalued rational series, i.e. mappings r:Σ∗→R computed by weighted automata. An algorithm is provided, that takes a weighted automaton A as input and halts if and only if the corresponding series rA is Absolutely convergent: hence, Absolute Convergence of rational series is semidecidable. A spectral radiuslike parameter ρr is introduced, which satisfies the following property: a rational series r is Absolutely convergent iff ρr<1. We show that if r is rational, then ρr can be approximated by convergent upper estimates. Then, it is shown that the sum Σw∈Σ∗r(w) can be estimated to any accuracy rate. This result can be extended to any sum of the form Σw∈Σ∗r(w)p, for any integer p.

Absolute Convergence of rational series is semi decidable
Language and Automata Theory and Applications, 2009CoAuthors: Raphael Bailly, Francois DenisAbstract:We study realvalued Absolutely convergent rational series , i.e. functions $r: {\it\Sigma}^* \rightarrow {\mathbb R}$, defined over a free monoid ${\it\Sigma}^*$, that can be computed by a multiplicity automaton A and such that $\sum_{w\in {\it\Sigma}^*}r(w) . We prove that any Absolutely convergent rational series r can be computed by a multiplicity automaton A which has the property that r A  is simply convergent, where r A  is the series computed by the automaton A  derived from A by taking the Absolute values of all its parameters. Then, we prove that the set ${\cal A}^{rat}({\it\Sigma})$ composed of all Absolutely convergent rational series is semidecidable and we show that the sum $\sum_{w\in \Sigma^*}r(w)$ can be estimated to any accuracy rate for any $r\in {\cal A}^{rat}({\it\Sigma})$. We also introduce a spectral radiuslike parameter ρ r  which satisfies the following property: r is Absolutely convergent iff ρ r  < 1.
Werner E G Muller – One of the best experts on this subject based on the ideXlab platform.

on the spectral side of arthur s trace formula Absolute Convergence
Annals of Mathematics, 2011CoAuthors: Tobias Finis, Erez Lapid, Werner E G MullerAbstract:We derive a renement of the spectral expansion of Arthur’s trace formula. The expression is Absolutely convergent with respect to the trace norm.
Raphael Bailly – One of the best experts on this subject based on the ideXlab platform.

Absolute Convergence of rational series is semi decidable
Information & Computation, 2011CoAuthors: Raphael Bailly, Francois DenisAbstract:This paper deals with Absolute Convergence of realvalued rational series, i.e. mappings r:Σ∗→R computed by weighted automata. An algorithm is provided, that takes a weighted automaton A as input and halts if and only if the corresponding series rA is Absolutely convergent: hence, Absolute Convergence of rational series is semidecidable. A spectral radiuslike parameter ρr is introduced, which satisfies the following property: a rational series r is Absolutely convergent iff ρr<1. We show that if r is rational, then ρr can be approximated by convergent upper estimates. Then, it is shown that the sum Σw∈Σ∗r(w) can be estimated to any accuracy rate. This result can be extended to any sum of the form Σw∈Σ∗r(w)p, for any integer p.

Absolute Convergence of rational series is semi decidable
Language and Automata Theory and Applications, 2009CoAuthors: Raphael Bailly, Francois DenisAbstract:We study realvalued Absolutely convergent rational series , i.e. functions $r: {\it\Sigma}^* \rightarrow {\mathbb R}$, defined over a free monoid ${\it\Sigma}^*$, that can be computed by a multiplicity automaton A and such that $\sum_{w\in {\it\Sigma}^*}r(w) . We prove that any Absolutely convergent rational series r can be computed by a multiplicity automaton A which has the property that r A  is simply convergent, where r A  is the series computed by the automaton A  derived from A by taking the Absolute values of all its parameters. Then, we prove that the set ${\cal A}^{rat}({\it\Sigma})$ composed of all Absolutely convergent rational series is semidecidable and we show that the sum $\sum_{w\in \Sigma^*}r(w)$ can be estimated to any accuracy rate for any $r\in {\cal A}^{rat}({\it\Sigma})$. We also introduce a spectral radiuslike parameter ρ r  which satisfies the following property: r is Absolutely convergent iff ρ r  < 1.