The Bohr radius of the nn-dimensional polydisk is equivalent to log⁡nn\sqrt{\frac{\log n}{n}}

We show that the Bohr radius of the polydisk $\mathbb D^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential.Comment: The introduction was expanded and some misprints correcte

On a conjecture regarding the upper graph box dimension of bounded subsets of the real line

Let X \subset R be a bounded set; we introduce a formula that calculates the upper graph box dimension of X (i.e.the supremum of the upper box dimension of the graph over all uniformly continuous functions defined on X). We demonstrate the strength of the formula by calculating the upper graph box dimension for some sets and by giving an "one line" proof, alternative to the one given in [1], of the fact that if X has finitely many isolated points then its upper graph box dimension is equal to the upper box dimension plus one. Furthermore we construct a collection of sets X with infinitely many isolated points, having upper box dimension a taking values from zero to one while their graph box dimension takes any value in [max{2a,1},a + 1], answering this way, negatively to a conjecture posed in [1]

Recurrence properties of hypercyclic operators

[EN] We generalize the notions of hypercyclic operators, U-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics, namely A-hypercyclicity. We then state an A-hypercyclicity criterion, inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion, and we show that this criterion characterizes the A-hypercyclicity for weighted shifts. We also investigate which density properties can the sets N(x, U) = {n is an element of N; T-n x is an element of U} have for a given hypercyclic operator, and we study the new notion of reiteratively hypercyclic operators.This work is supported in part by MEC and FEDER, Project MTM2013-47093-P, and by GVA, Projects PROMETEOII/2013/013 and ACOMP/2015/005. The second author was a postdoctoral researcher of the Belgian FNRS.Bès, JP.; Menet, Q.; Peris Manguillot, A.; Puig-De Dios, Y. (2016). Recurrence properties of hypercyclic operators. Mathematische Annalen. 366(1):545-572. https://doi.org/10.1007/s00208-015-1336-3S5455723661Badea, C., Grivaux, S.: Unimodular eigenvalues, uniformly distributed sequences and linear dynamics. Adv. Math. 211, 766–793 (2007)Bayart, F., Grivaux, S.: Frequently hypercyclic operators. Trans. Amer. Math. Soc. 358, 5083–5117 (2006)Bayart, F., Grivaux, S.: Invariant Gaussian measures for operators on Banach spaces and linear dynamics. Proc. Lond. Math. Soc. 94, 181–210 (2007)Bayart, F., Matheron, É.: Dynamics of linear operators, Cambridge Tracts in Mathematics, 179. Cambridge University Press, Cambridge (2009)Bayart, F., Matheron, É.: (Non-)weakly mixing operators and hypercyclicity sets. Ann. Inst. Fourier 59, 1–35 (2009)Bayart, F., Ruzsa, I.: Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory Dynam. Syst. 35, 691–709 (2015)Bergelson, V.: Ergodic Ramsey Theory- an update, Ergodic Theory of $$\mathbb{Z}^d$$ Z d -actions. Lond. Math. Soc. Lecture Note Ser. 28, 1–61 (1996)Bernal-González, L., Grosse-Erdmann, K.-G.: The Hypercyclicity Criterion for sequences of operators. Studia Math. 157, 17–32 (2003)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors. Ergodic Theory Dynam. Syst. 27, 383–404 (2007)Bonilla, A., Grosse-Erdmann, K.-G.: Erratum: Ergodic Theory Dynam. Systems 29, 1993–1994 (2009)Chan, K., Seceleanu, I.: Hypercyclicity of shifts as a zero-one law of orbital limit points. J. Oper. Theory 67, 257–277 (2012)Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Amer. Math. Soc. 132, 385–389 (2004)Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton (1981)Giuliano, R., Grekos, G., Mišík, L.: Open problems on densities II, Diophantine Analysis and Related Fields 2010. AIP Conf. Proc. 1264, 114–128 (2010)Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139, 47–68 (2000)Grosse-Erdmann, K.-G., Peris, A.: Frequently dense orbits. C. R. Math. Acad. Sci. Paris 341, 123–128 (2005)Grosse-Erdmann, K.G., Peris, A.: Weakly mixing operators on topological vector spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 104, 413–426 (2010)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos, Universitext. Springer, London (2011)Menet, Q.: Linear chaos and frequent hypercyclicity. Trans. Amer. Math. Soc. arXiv:1410.7173Puig, Y.: Linear dynamics and recurrence properties defined via essential idempotents of $$\beta {\mathbb{N}}$$ β N (2014) arXiv:1411.7729 (preprint)Salas, H.N.: Hypercyclic weighted shifts. Trans. Amer. Math. Soc. 347, 993–1004 (1995)Salat, T., Toma, V.: A classical Olivier’s theorem and statistical convergence. Ann. Math. Blaise Pascal 10, 305–313 (2003)Shkarin, S.: On the spectrum of frequently hypercyclic operators. Proc. Am. Math. Soc. 137, 123–134 (2009

Almost sure-sign convergence of Hardy-type Dirichlet series

[EN] Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series is uniformly a.s.- sign convergent (i.e., converges uniformly for almost all sequences of signs epsilon (n) = +/- 1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space.Supported by CONICET-PIP 11220130100329CO, PICT 2015-2299 and UBACyT 20020130100474BA. Supported by MICINN MTM2017-83262-C2-1-P. Supported by MICINN MTM2017-83262-C2-1-P and UPV-SP20120700.Carando, D.; Defant, A.; Sevilla Peris, P. (2018). Almost sure-sign convergence of Hardy-type Dirichlet series. Journal d Analyse Mathématique. 135(1):225-247. https://doi.org/10.1007/s11854-018-0034-yS2252471351A. Aleman, J.-F. Olsen, and E. Saksman, Fourier multipliers for Hardy spaces of Dirichlet series, Int. Math. Res. Not. IMRN 16 (2014), 4368–4378.R. Balasubramanian, B. Calado, and H. Queffélec, The Bohr inequality for ordinary Dirichlet series Studia Math. 175 (2006), 285–304.F. Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), 203–236.F. Bayart, A. Defant, L. Frerick, M. Maestre, and P. Sevilla-Peris, Monomial series expansion of Hp-functions and multipliers ofHp-Dirichlet series, Math. Ann. 368 (2017), 837–876.F. Bayart, D. Pellegrino, and J. B. Seoane-Sepúlveda, The Bohr radius of the n-dimensional polydisk is equivalent to $$\sqrt {\left( {\log n} \right)/n}$$ ( log n ) / n , Adv. Math. 264 (2014), 726–746.F. Bayart, H. Queffélec, and K. Seip, Approximation numbers of composition operators on Hp spaces of Dirichlet series, Ann. Inst. Fourier (Grenoble) 66 (2016), 551–588.H. F. Bohnenblust and E. Hille. On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), 600–622.H. Bohr, Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum {\frac{{{a_n}}}{{{n^s}}}}$$ ∑ a n n s , Nachr. Ges.Wiss. Göttingen, Math. Phys. Kl., 1913, pp. 441–488.D. Carando, A. Defant, and P. Sevilla-Peris, Bohr’s absolute convergence problem for Hp- Dirichlet series in Banach spaces, Anal. PDE 7 (2014), 513–527.D. Carando, A. Defant, and P. Sevilla-Peris, Some polynomial versions of cotype and applications, J. Funct. Anal. 270 (2016), 68–87.B. J. Cole and T. W. Gamelin, Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. London Math. Soc. (3) 53 (1986), 112–142.R. de la Bretèche. Sur l’ordre de grandeur des polynômes de Dirichlet, Acta Arith. 134 (2008), 141–148.A. Defant, L. Frerick, J. Ortega-Cerdà, M. Ounäies, and K. Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), 485–497.A. Defant, D. García, M. Maestre, and D. Pérez-García, Bohr’s strip for vector valued Dirichlet series, Math. Ann. 342 (2008), 533–555.A. Defant, M. Maestre, and U. Schwarting, Bohr radii of vector valued holomorphic functions, Adv. Math. 231 (2012), 2837–2857.A. Defant and A. Pérez, Hardy spaces of vector-valued Dirichlet series, StudiaMath. (to appear), 2018 DOI: 10.4064/sm170303-26-7.A. Defant, U. Schwarting, and P. Sevilla-Peris, Estimates for vector valued Dirichlet polynomials, Monatsh. Math. 175 (2014), 89–116.J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, 1995.P. Hartman, On Dirichlet series involving random coefficients, Amer. J. Math. 61 (1939), 955–964.H. Hedenmalm, P. Lindqvist, and K. Seip, A Hilbert space of Dirichlet series and systems of dilated functions in L2(0, 1), Duke Math. J. 86 (1997), 1–37.A. Hildebrand, and G. Tenenbaum, Integers without large prime factors, J. Thor. Nombres Bordeaux 5 (1993), 411–484.S. V. Konyagin and H. Queffélec, The translation 1/2 in the theory of Dirichlet series, Real Anal. Exchange 27 (2001/02) 155–175.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Springer-Verlag, Berlin, 1979.B. Maurizi and H. Queffélec, Some remarks on the algebra of bounded Dirichlet series, J. Fourier Anal. Appl. 16 (2010), 676–692.H. Queffélec, H. Bohr’s vision of ordinary Dirichlet series; old and new results, J. Anal. 3 (1995), 43–60.H. Queffélec and M. Queffélec, Diophantine Approximation and Dirichlet Series, Hindustan Book Agency, New Delhi, 2013.G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, Cambridge, 1995

Portugal and Angola: the politics of a troubled media relationship

In his last text of 2016, published on Christmas day, the editor of Angola’s official newspaper, Jornal de Angola, wrote a ‘message of harmony’ where he chose to focus on diplomatic relations with the former colonial power. José Ribeiro’s reading was clear: “Forty one years after independence the Portuguese elites still treat us impolitely as if we were their slaves” (Ribeiro, 2016). This posture would be reinforced precisely a week later in the first editorial of 2017: “Angola will not cease to be an independent country (…) no longer willing to accept mouldy neo-colonial impositions from abroad” (Ribeiro, 2017).(undefined)info:eu-repo/semantics/publishedVersio

Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \mathbb{C}^\mathbb{N}. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator.This work was partially supported by ANR-Projet Blanc DYNOP, by the MEC and FEDER Projects MTM2007-64222 and MTM2010-14909, and by Generalitat Valenciana Project PROMETEO/2008/101.De La Rosa Penilla, M.; Frerick, L.; Grivaux, S.; Peris Manguillot, A. (2012). Frequent hypercyclicity, chaos, and unconditional Schauder decompositions. Israel Journal of Mathematics. 190(1):389-399. https://doi.org/10.1007/s11856-011-0210-6S3893991901S. Ansari, Existence of hypercyclic operators on topological vector spaces, Journal of Functional Analysis 148 (1997), 384–390.F. Bayart and S. Grivaux, Frequently hypercyclic operators, Transactions of the American Mathematical Society 358 (2006), 5083–5117.F. Bayart and S. Grivaux, Hypercyclicity and unimodular point spectrum, Journal of Functional Analysis 226 (2005), 281–300.F. Bayart and S. Grivaux, Invariant Gaussian measures for linear operators on Banach spaces and linear dynamics, Proceedings of the London Mathematical Society 94 (2007), 181–210.F. Bayart and É. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.L. Bernal-González, On hypercyclic operators on Banach spaces, Proceedings of the American Mathematical Society 127 (1999), 1003–1010.J. Bès and A. Peris, Hereditarily hypercyclic operators, Journal of Functioanl Analysis 167 (1999), 94–112.J. Bonet, F. Martínez-Giménez and A. Peris, A Banach space wich admits no chaotic operator, The Bulletin of the London Mathematical Society 33 (2001), 196–198.M. De la Rosa, L. Frerick, S. Grivaux and A. Peris, Chaos on Fréchet spaces with unconditional basis, preprint.W. T. Gowers, A solution to Banach’s hyperplane problem, The Bulletin of the London Mathematical Society 26 (1994), 523–530.W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Mathematische Annalen 307 (1997), 543–568.W. T. Gowers and B. Maurey, The unconditional basic sequence problem, Journal of the American Mathematical Society 6 (1993), 851–874.S. Grivaux, A new class of frequently hypercyclic operators, Indiana University Mathematics Journal, to appear.K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer-Verlag, Berlin, 2011.K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs, New Series, Vol. 20, Clarendon Press, Oxford, 2000.S. Shkarin, On the spectrum of frequently hypercyclic operators, Proceedings of the American Mathematical Society 137 (2009), 123–134

A note on abscissas of Dirichlet series

[EN] We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce and study weak versions of the abscissas for scalar-valued Dirichlet series.A. Defant: Partially supported by MINECO and FEDER MTM2017-83262-C2-1-P. A. Pérez: Supported by La Caixa Foundation, MINECO and FEDER MTM2014-57838-C2-1-P and Fundación Séneca - Región de Murcia (CARM 19368/PI/14). P. Sevilla-Peris: Supported by MINECO and FEDER MTM2017-83262-C2-1-P.Defant, A.; Pérez, A.; Sevilla Peris, P. (2019). A note on abscissas of Dirichlet series. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(3):2639-2653. https://doi.org/10.1007/s13398-019-00647-yS263926531133Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Mon. Math. 136(3), 203–236 (2002)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann Math. 32(3), 600–622 (1931)Bohr, H.: Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum \,\frac{a_n}{n^s}$$ ∑ a n n s . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., pp. 441–488 (1913)Bonet, J.: Abscissas of weak convergence of vector valued Dirichlet series. J. Funct. Anal. 269(12), 3914–3927 (2015)Carando, D., Defant, A., Sevilla-Peris, P.: Bohr’s absolute convergence problem for $$\cal{H}_p$$ H p -Dirichlet series in Banach spaces. Anal. PDE 7(2), 513–527 (2014)Carando, D., Defant, A., Sevilla-Peris, P.: Some polynomial versions of cotype and applications. J. Funct. Anal. 270(1), 68–87 (2016)Defant, A., García, D., Maestre, M., Pérez-García, D.: Bohr’s strip for vector valued Dirichlet series. Math. Ann. 342(3), 533–555 (2008)Defant, A., García, D., Maestre, M., Sevilla–Peris, P.: Dirichlet Series and Holomorphic Funcions in High Dimensions, vol. 37 of New Mathematical Monographs. Cambridge University Press, Cambridge (2019)Defant, A., Pérez, A.: Optimal comparison of the $$p$$ p -norms of Dirichlet polynomials. Israel J. Math. 221(2), 837–852 (2017)Defant, A., Pérez, A.: Hardy spaces of vector-valued Dirichlet series. Studia Math. 243(1), 53–78 (2018)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators, vol. 43 of Cambridge studies in advanced mathematics. Cambridge University Press, Cambridge (1995)Maurizi, B., Queffélec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676–692 (2010)Queffélec, H., Queffélec, M.: Diophantine approximation and Dirichlet series, vol. 2 of Harish–Chandra research institute lecture notes. Hindustan Book Agency, New Delhi (2013

Two 'transitions': the political economy of Joyce Banda's rise to power and the related role of civil society organisations in Malawi

This is an Accepted Manuscript of an article published by Taylor & Francis in Review of African Political Economy on 21/07/2014, available online: http://www.tandfonline.com/doi/abs/10.1080/03056244.2014.90194

Nigerian scam e-mails and the charms of capital

So-called '419' or 'advance-fee' e-mail frauds have proved remarkably successful. Global losses to these scams are believed to run to billions of dollars. Although it can be assumed that the promise of personal gain which these e-mails hold out is part of what motivates victims, there is more than greed at issue here. How is it that the seemingly incredible offers given in these unsolicited messages can find an audience willing to treat them as credible? The essay offers a speculative thesis in answer to this question. Firstly, it is argued, these scams are adept at exploiting common presuppositions in British and American culture regarding Africa and the relationships that are assumed to exist between their nations and those in the global south. Secondly, part of the appeal of these e-mails lies in the fact that they appear to reveal the processes by which wealth is created and distributed in the global economy. They thus speak to their readers’ attempts to map or conceptualise the otherwise inscrutable processes of that economy. In the conclusion the essay looks at the contradictions in the official state response to this phenomena