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Absolute Convergence

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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, 2011
    Co-Authors: Raphael Bailly, Francois Denis
    Abstract:

    This paper deals with Absolute Convergence of real-valued 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 semi-decidable. A spectral radius-like parameter ρ|r| is introduced, which satisfies the following property: a rational series r is Absolutely convergent iff ρ|r|<1. We show that if r is rational, then ρ|r| 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, 2009
    Co-Authors: Raphael Bailly, Francois Denis
    Abstract:

    We study real-valued 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 semi-decidable 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 radius-like 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, 2011
    Co-Authors: Tobias Finis, Erez Lapid, Werner E G Muller
    Abstract:

    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, 2011
    Co-Authors: Raphael Bailly, Francois Denis
    Abstract:

    This paper deals with Absolute Convergence of real-valued 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 semi-decidable. A spectral radius-like parameter ρ|r| is introduced, which satisfies the following property: a rational series r is Absolutely convergent iff ρ|r|<1. We show that if r is rational, then ρ|r| 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, 2009
    Co-Authors: Raphael Bailly, Francois Denis
    Abstract:

    We study real-valued 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 semi-decidable 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 radius-like parameter ρ |r | which satisfies the following property: r is Absolutely convergent iff ρ |r | < 1.

Somesh K Mathur – One of the best experts on this subject based on the ideXlab platform.

  • Absolute Convergence its speed and economic growth for selected countries for 1961 2001
    Korea and the World Economy, 2005
    Co-Authors: Somesh K Mathur
    Abstract:

    We use cross sectional data of GDP per capita levels and growth rates of European countries EU16 (EU15 + UK), South Asian Countries (5), some East Asian (8) and CIS Countries (15) to test for ‘Absolute Convergence’ hypothesis for four different periods 19612001,1970-2001,1980-2001,1990-2001. Only EU and East Asian countries together have shown uniform evidence of Absolute Convergence in all periods. While EU as a region has shown significant evidence of Absolute Convergence in two periods, 19612001 and 1970-2001, there is no convincing statistical evidence in favor of Absolute Convergence in the last two periods: 1980-2001 and 1990-2001. This latter evidence with declining rate of economic growth for EU since 1961 points to a challenge for designing EUs regional policies which also have to cope up with many East European and Baltic nations who joined EU recently. The speed of Absolute Convergence in the four periods range between 0.99-2.56% p.a. (2% for the EU was worked out by Barro and Xavier Sala-iMartin(1995) for European regions) for EU while it ranges between 0.57-1.16% p.a. for the countries in East Asia and EU regions together. However, there is no evidence of Convergence among the South Asian countries in all periods and some major CIS republics since 1966. There is however tendency for Absolute Convergence among countries of South Asia, East Asia and European Union together particularly after the 1980s.

  • Absolute and conditional Convergence its speed for selected countries for 1961 2001
    Social Science Research Network, 2005
    Co-Authors: Somesh K Mathur
    Abstract:

    The study gives the theoretical justification for the per capita growth equations using Solovian model(1956) and its factor accumulation assumptions. The different forms of the per capita growth equation is used to test for ‘Absolute Convergence‘ and ‘conditional Convergence‘ hypotheses and also work out the speed of Absolute and conditional Convergence for selected countries from 1961-2001.We use cross sectional data of GDP per capita levels and growth rates of European countries EU16(EU15 +United Kingdom), South Asian Countries (5), some East Asian (8) and CIS Countries (15) to test for ‘Absolute Convergence‘ hypothesis for four different periods 1961-2001,1970-2001,1980-2001,1990-2001.Only EU and East Asian countries together have shown uniform evidence of Absolute Convergence in all periods. While EU as a region has shown significant evidence of Absolute Convergence in two periods, 1961-2001 and 1970-2001, there is no convincing statistical evidence in favor of Absolute Convergence in the last two periods: 1980-2001 and 1990- 2001.This latter evidence with declining rate of economic growth for EU since 1961 points to a challenge for designing EUs regional policies which also have to cope up with many East European and Baltic nations who joined EU recently. The speed of Absolute Convergence in the four periods range between 0.99-2.56 % p.a. (2% for the EU was worked out by Barro and Xavier Sala-i-Martin, 1995, for European regions) for EU while it ranges between 0.57-1.16 % p.a. for the countries in East Asia and EU regions together. However, there is no evidence of Convergence among the South Asian countries in all periods and some major CIS republics since 1966.There is however tendency for Absolute Convergence among countries of South Asia, East Asia and European Union together particularly after the 1980s. Conditional Convergence is prevalent among almost all pairs of regions in our sample except East Asian and South Asian nations together.Speed of conditional Convergence ranges from 0.2 % in an year to 22%.In the European nations, the speed of conditional Convergence works out be nearly 20 % unlike the speed of Absolute Convergence which hovered around 2 %.Such results would mean that countries in Europe are converging very quickly to their own potential level of incomes per capita but not so quickly to a common potential level of income per capita.The elasticity of output which is also estimated ranges from 0.54 to 0.91 implying that capital is to be interpreted as broad capital inclusive of human capicapital stock.It seems that human capital not only affects technological progress but affects output levels directly by increasing capital stock levels implying that the assumption of including human capicapital stock in the production function were appropriate in Mankiw,Romer and Weil(1992). The results for the speed of conditional Convergence favors use of an extended Solovian model inclusive of human capital.Conditional beta Convergence seems to be a better empirical exercise(as evident from our theoretical model and empirical results ) because it reflects the Convergence of countries after we control for differences in steady states .Conditional Convergence is simply a confirmation of a result predicted by the neoclassical growth model:that countries with similar steady states exhibit Convergence.It does not mean that all countries in the world are converging to the same steady state,only that they are converging to their own steady states

Erez Lapid – 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, 2011
    Co-Authors: Tobias Finis, Erez Lapid, Werner E G Muller
    Abstract:

    We derive a renement of the spectral expansion of Arthur’s trace formula. The expression is Absolutely convergent with respect to the trace norm.

  • on the Absolute Convergence of the spectral side of the arthur trace formula for gl n
    arXiv: Representation Theory, 2002
    Co-Authors: Werner Mueller, Birgit Speh, Erez Lapid
    Abstract:

    Let G be the group GL(n) over a number field E and let A be the ring of adeles of E. In this paper we prove that the spectral side of the Arthur trace formula for G is Absolutely convergent for all integrable rapidly decreasing functions on $G(A)^1$.