the inclusion problem for mixed norm spaces given two mixed norm lebesgue spaces on an n fold product of arbitrary finite measure spaces when is one contained in the other if so what is the norm of the inclusion map these questions are answered completely for a large range of lebesgue indices and all measure spaces when the measure spaces are atomless both questions are settled for all indices when the measure spaces are not purely atomic the first question is settled for all indices some complete and some partial results are given in the remaining cases but a wide variety of behaviour is observed in particular the norm problem for purely atomic measure spaces is seen to be intractable for certain ranges of the lebesgue indices it is equivalent to an optimization problem that includes a known np hard problem as a special case

bohr inequalities for free holomorphic functions on polyballs abstract multivariable operator theory is used to provide bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball b n n n 1 n k n k which is a noncommutative analogue of the scalar polyball c n 1 1 c n k 1 the bohr radius k m h b n resp k h b n associated with the multi homogeneous resp homogeneous power series expansions of the free holomorphic functions are the main objects of study in this paper we extend a theorem of bombieri and bourgain for the disc d z c z 1 to the polyball and obtain the estimations 1 3 k k m h b n 2 log k k if k 1 extending boas khavinson result for the scalar polydisc d k with respect to the homogeneous power series expansion we prove that k h b n 1 3 extending the classical result and obtain analogues of caratheodory fejer and egervary szasz inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball these results are used to provide multivariable analogues of landau s inequality and bohr s inequality when the norm is replaced by the numerical radius of an operator when specialized to the regular polydisc d k which corresponds to the case n 1 n k 1 we obtain new results concerning bohr landau fejer and harnack inequalities for operator valued holomorphic functions and k pluriharmonic functions on the scalar polydisc d k the results of the paper can be used to obtain bohr type inequalities for the noncommutative ball algebra a n the hardy algebra f n and the c algebra c s generated by the universal model s of the polyball b n

moduli spaces and castelnuovo mumford regularity of sheaves on surfaces we generalize donaldson gieseker li and o grady s results on generic smoothness of the moduli spaces of sheaves with fixed determinant and large discriminant to positive characteristic we also show optimal bounds on the castelnuovo mumford regularity of sheaves on surfaces and we use it to give the first general effective results on irreducibility of the moduli spaces

there exist multilinear bohnenblust hille constants cn n 1 with limn cn 1 cn 0 abstract the n linear bohnenblust hille inequality asserts that there is a constant c n 1 such that the l 2 n n 1 norm of u e i 1 e i n i 1 i n 1 n is bounded above by c n times the supremum norm of u for any n linear form u c n c n c and n n the same holds for real scalars we prove what we call fundamental lemma which brings new information on the optimal constants k n n 1 for both real and complex scalars for instance k n 1 k n 0 87 n 0 473 for infinitely many n s for complex scalars we give a formula of surprisingly low growth in which e and the famous euler mascheroni constant appear k n 1 4 1 e 2 1 2 j 1 n 1 j log 2 e 2 1 2 1 n 2 we study the interplay between the kahane salem zygmund and the bohnenblust hille polynomial and multilinear inequalities and provide estimates for bohnenblust hille type inequality constants for any exponent q 2 n n 1

a subexponential vector valued bohnenblust hille type inequality abstract bayart pellegrino and seoane recently proved that the polynomial bohnenblust hille inequality for complex scalars is subexponential we show that a vector valued polynomial bohnenblust hille inequality on complex banach lattices is also subexponential for some special cases our main result recovers the best known constants of the classical polynomial inequality provided in 4

the period index problem for fields of transcendence degree 2 using geometric methods we prove the standard period index conjecture for the brauer group of a field of transcendence degree 2 over fp

generalization of a theorem of bohr for bases in spaces of holomorphic functions of several complex variables abstract in the first part we generalize the classical result of bohr by proving that an analogous phenomenon occurs whenever d is an open domain in c m or more generally a complex manifold and n n 0 is a basis in the space of holomorphic functions h d such that 0 1 and n z0 0 n 1 for some z0 d namely then there exists a neighborhood u of the point z0 such that whenever a holomorphic function on d has modulus less than 1 the sum of the suprema in u of the moduli of the terms of its expansion is less than 1 too in the second part we consider some natural hilbert spaces of analytic functions and derive necessary and sufficient conditions for the occurrence of bohr s phenomenon in this setting

banach spaces of general dirichlet series abstract we study when the spaces of general dirichlet series bounded on a half plane are banach spaces and show that some of those classes are isometrically isomorphic between themselves in a precise way let n be a strictly increasing sequence of positive real numbers such that lim n n we denote by h n the complex normed space of all dirichlet series d s n b n n s which are convergent and bounded on the half plane re s 0 endowed with the norm d sup re s 0 d s if there exists q 0 such that inf n n 1 q n q 0 then h n is a banach space further if there exists a strictly increasing sequence r n of positive numbers such that the sequence log r n is q linearly independent n r for n p and n is the increasing rearrangement of the sequence n then h n is isometrically isomorphic to h b c 0 with this condition we explain more explicitly the optimal cases of the difference among the abscissas c b u and a

multiple rademacher means and their applications abstract we evaluate multiple rademacher means for various classes of multilinear operators under the assumption that the range has cotype q these results show that the class of multiple q 2 summing operators plays an important role further we get new extensions of bu s theorem in the multilinear case

the bohr radius of the n dimensional polydisk is equivalent to 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

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

coordinatewise multiple summing operators in banach spaces we invent the new notion of coordinatewise multiple summing operators in banach spaces and use it to study various vector valued extensions of the well know bohnenblust hille inequality which originally extended littlewood s 4 3 inequality our results have application on the summability of monomial coefficients of m homogeneous polynomials p l lp as well as for the convergence theory of products of vector valued dirichlet series

sharp bohr type inequality abstract this article is devoted to the sharp improvement of the classical bohr inequality for bounded analytic functions defined on the unit disk we also prove two other sharp versions of the bohr inequality by replacing the constant term by the absolute of the function and the square of the absolute of the function respectively

moduli of twisted orbifold sheaves abstract we study stacks of slope semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope semistable sheaves on smooth projective surfaces

modal trajectory estimation using maximum gaussian mixture this technical note deals with the estimation of the whole trajectory of a stochastic dynamic system with highest probability conditionally upon the past observation process using a maximum gaussian mixture we first recall the gaussian sum technique applied to minimum variance filtering it is then shown that the same concept of gaussian mixture can be applied in that context provided we replace the sum operator by the max operator

asymptotics of the bohr radius for polynomials of fixed degree we obtain a characterization and conjecture asymptotics of the bohr radius for the class of complex polynomials in one variable our work is based on the notion of bound preserving operators

approximating posterior distributions by mixtures kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions resulting in revised approximations that are mixtures of standard parametric forms usually multivariate normal or t distributions adaptive refinement of such mixture approximations involves repeating this process to home in successively on the posterior in fairly low dimensional problems this provides a general and automatic method of approximating posteriors by mixtures so that marginal densities and other summaries may be easily computed

factorization of absolutely continuous polynomials abstract in this paper we study the ideal of dominated p continuous polynomials that extend the nowadays well known ideal of p dominated polynomials to the more general setting of the interpolated ideals of polynomials we give the polynomial version of pietsch s factorization theorem for this new ideal although based on botelho et al in press 16 our factorization theorem requires new techniques inspired in the theory of banach lattices

improving the closed formula for subpolynomial constants in the multilinear bohnenblust hille inequalities abstract for k r or c the bohnenblust hille inequality asserts that there exists a sequence of scalars c k m m 1 such that i 1 i m 1 n u e i 1 e i m 2 m m 1 m 1 2 m c k m sup z 1 z m d n tu z 1 z m for all m linear forms u k n k n k and every positive integer n where e i i 1 n denotes the canonical basis of k n and d n represents the open unit polydisc in k n very recently 2012 it was shown that there exist constants c k m m 1 with subpolynomial growth satisfying this inequality however these constants were obtained via a complicated recursive formula we improve the best known closed non recursive approximation for these constants

mode finding for mixtures of gaussian distributions gradient quadratic and fixed point iteration algorithms and appropriate values for their control parameters are derived for finding all modes of a gaussian mixture a problem with applications in clustering and regression the significance of the modes found is quantified locally by hessian based error bars and globally by the entropy as sparseness measure

groupe de picard des varietes de modules de fibres semi stables sur les courbes algebriques soient x une courbe algebrique projective lisse de genre g 2 sur r d des entiers avec r 2 on note u r d la variete de modules des fibres algebriques semi stables sur x de rang r et de degre d us r d l ouvert de u r d correspondant aux fibres stables on sait que u r d est une variete algebrique projective irreductible et normale si r et d ne sont pas premiers entre eux u r d n est pas lisse sauf dans une exception le cas ou g 2 r 2 et d est pair on supposera dans cet article qu on n est pas dans ce cas on a alors codimu r d u r d us r d 2 et u r d us r d est le lieu des points singuliers de u r d si l est un fibre en droites de degre d sur x on note u r l la sous variete fermee de u r d correspondant aux fibres vectoriels de determinant isomorphe a l on etudie dans cet article les groupes de picard pic u r d et pic u r l on montre d abord que les varietes u r d et u r l sont localement factorielles on calcule ensuite pic u r d et pic u r l qui sont decrits au moyen des diviseurs thetas generalises

maximum a posteriori state path estimation discretization limits and their interpretation continuous discrete models with dynamics described by stochastic differential equations are used in a wide variety of applications for these systems the maximum a posteriori map state path can be defined as the curves around which lie the infinitesimal tubes with greatest posterior probability which can be found by maximizing a merit function built upon the onsager machlup functional a common approach used in the engineering literature to obtain the map state path is to discretize the dynamics and obtain the map state path for the discretized system in this paper we prove that if the trapezoidal scheme is used for discretization then the discretized map state path estimation converges hypographically to the continuous discrete map state path estimation as the discretization gets finer however if the stochastic euler scheme is used instead then the discretized estimation converges to the minimum energy estimation the minimum energy estimates are in turn proved to be the state paths associated with the map noise paths which in some cases differ from the map state paths therefore the discretized map state paths can have different interpretations depending on the discretization scheme used

a new multilinear insight on littlewood s 4 3 inequality abstract we unify littlewood s classical 4 3 inequality a forerunner of grothendieck s inequality together with its m linear extension due to bohnenblust and hille which originally settled bohr s absolute convergence problem for dirichlet series with a scale of inequalties of bennett and carl in l p spaces which are of fundamental importance in the theory of eigenvalue distribution of power compact operators as an application we give estimates for the monomial coefficients of homogeneous l p valued polynomials on c 0

the asymptotic growth of the constants in the bohnenblust hille inequality is optimal the search of sharp estimates for the constants in the bohnenblust hille inequality besides its challenging nature has quite important applications in different fields of mathematics and physics for homogeneous polynomials it was recently shown that the bohnenblust hille inequality for complex scalars is hypercontractive this result interesting by itself has found direct striking applications in the solution of several important problems for multilinear mappings precise information on the asymptotic behavior of the constants of the bohnenblust hille inequality is of particular importance for applications in quantum information theory and multipartite bell inequalities in this paper using elementary tools we prove a quite surprising result the asymptotic growth of the constants in the multilinear bohnenblust hille inequality is optimal besides its intrinsic mathematical interest and potential applications to different areas the mathematical importance of this result also lies in the fact that all previous estimates and related results for the last 80 years such as for instance the multilinear version of the famous grothendieck theorem for absolutely summing operators always present constants c m s growing at an exponential rate of certain power of m

absolutely summing multilinear operators via interpolation abstract we use an interpolative technique from 1 to introduce the notion of multiple n separately summing operators our approach extends and unifies some recent results for instance we recover the best known estimates of the multilinear bohnenblust hille constants due to f bayart d pellegrino and j seoane sepulveda more precisely as a consequence of our main result for 1 t 2 and m 1 we prove that i 1 i m 1 u e i 1 e i m 2 t m 2 m 1 t 2 m 1 t 2 t m j 2 m 2 2 t j t 2 t 2 t j 2 2 2 t 2 j t u for all complex m linear forms u c 0 c 0 c

multipliers of dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables let mathscr h infty be the set of all ordinary dirichlet series d sum n a n n s representing bounded holomorphic functions on the right half plane a completely multiplicative sequence b n of complex numbers is said to be an ell 1 multiplier for mathscr h infty whenever sum n a n b n infty for every d in mathscr h infty we study the problem of describing such sequences b n in terms of the asymptotic decay of the subsequence b p j where p j denotes the jth prime number given a completely multiplicative sequence b b n we prove among other results b is an ell 1 multiplier for mathscr h infty provided b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 1 and conversely if b is an ell 1 multiplier for mathscr h infty then b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 le 1 here b stands for the decreasing rearrangement of b following an ingenious idea of harald bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk mathbb d infty the open unit ball of ell infty for which every bounded and holomorphic function f on mathbb d infty has an absolutely convergent monomial series expansion sum alpha frac partial alpha f 0 alpha z alpha moreover we study analogous problems in hardy spaces of dirichlet series and hardy spaces of functions on the infinite dimensional polytorus mathbb t infty

unconditional basis and gordon lewis constants for spaces of polynomials abstract no infinite dimensional banach space x is known which has the property that for m 2 the banach space of all continuous m homogeneous polynomials on x has an unconditional basis following a program originally initiated by gordon and lewis we study unconditionality in spaces of m homogeneous polynomials and symmetric tensor products of order m in banach spaces we show that for each banach space x which has a dual with an unconditional basis x i the approximable nuclear m homogeneous polynomials on x have an unconditional basis if and only if the monomial basis with respect to x i is unconditional moreover we determine an asymptotically correct estimate for the unconditional basis constant of all m homogeneous polynomials on l n p and use this result to narrow down considerably the list of natural candidates x with the above property

on summability of nonlinear mappings a new approach the main goal of this paper is to characterize arbitrary nonlinear non multilinear mappings f x 1 times cdots times x n rightarrow y between banach spaces that satisfy a quite natural pietsch domination type theorem around a given point a 1 ldots a n in x 1 times cdots times x n as a consequence of our approach a notion of weighted summability arises naturally which may be an interesting topic for further investigation

moduli of high rank vector bundles over surfaces the purpose of this work is to apply the degeneration theory developed in gl to study the moduli space of stable vector bundles of arbitrary rank on any smooth algebraic surface over c we will show that most of the recent progress in understanding moduli of rank two vector bundles can be carried over to high rank cases after introducing the notion of stable vector bundles the first author constructed the moduli schemes of vector bundles on surfaces he showed that for any smooth algebraic surface x with ample divisor h and line bundle i on x there is a coarse moduli scheme m x i h parameterizing modulo equivalence relation the set of all h semistable rank r torsion free sheaves e on x with dete i and c2 e d since then many mathematicians have studied the geometry of this moduli space especially for the rank two case to cite a few maruyama taubes and the first author showed that the moduli space m x m r d x i h is non empty when d is large moduli spaces of vector bundles of some special surfaces have been studied also the deep understanding of m x for arbitrary x and r 2 begins with donaldson s generic smoothness result roughly speaking donaldson do later generalized by friedman fr and k zhu zh showed that when d is large enough then the singular locus sing m x of m x is a proper subset of m 2 d x and its codimension in m x increases linearly in d this theorem indicates that the moduli m x behaves as expected when the second chern class d is large later using general deformation theory the second author proved that m x is normal and has local complete intersection l c i singularities at stable sheaves provided d is large l2 he also showed that when x is a surface of general type satisfying some mild technical conditions then m x is of general type for d 0 l2 in our paper gl we also proved that m x is irreducible if d is large in this and subsequent papers we shall show that the geometry of m x and the geometry of m x r 3 is rather similar the main obstacle in doing so is the lack of an analogy of the generic smoothness result in high rank case in this paper we will use the degeneration of moduli developed in gl to establish the following main technical theorem

bohr s strip for vector valued dirichlet series bohr showed that the width of the strip in the complex plane on which a given dirichlet series sum a n n s s in mathbb c converges uniformly but not absolutely is at most 1 2 and bohnenblust hille that this bound in general is optimal we prove that for a given infinite dimensional banach space y the width of bohr s strip for a dirichlet series with coefficients an in y is bounded by 1 1 cot y where cot y denotes the optimal cotype of y this estimate even turns out to be optimal and hence leads to a new characterization of cotype in terms of vector valued dirichlet series

on the bohnenblust hille inequality and a variant of littlewoodʼs 4 3 inequality the search for sharp constants for inequalities of the type littlewood s 4 3 and bohnenblust hille has lately shown unexpected applications in many fields such as analytic number theory quantum information theory or in results on n dimensional bohr radii recent estimates obtained for the multilinear bohnenblust hille inequality for real scalars have been used as a crucial tool by a montanaro in order to solve problems in quantum xor games here among other results we obtain new upper bounds for the bohnenblust hille constants for complex scalars for bilinear forms we provide optimal constants of variants of littlewood s 4 3 inequality for real scalars when the exponent 4 3 is replaced by any r 4 3 we also prove that the optimal constants in real case are always strictly greater than those from the complex case

reinhardt domains of holomorphy in banach spaces abstract it is known that in c 0 the holomorphic functions representable by multiple power series the series of monomials are those of nuclear type in this article we show that in a banach space with unconditional schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and in fact the domain of convergence of such a series

summing multilinear operators by blocks the isotropic and anisotropic cases abstract unifying several directions of the development of the study of summing multilinear operators between banach spaces we construct a general framework that studies under one single definition multilinear operators that are summing with respect to sums taken over any number of indices iterated and non iterated sums the isotropic and the anisotropic cases sums over arbitrary blocks and over several different sequence norms a large number of special classes of multilinear operators and of methods of generating classes of multilinear operators are recovered as particular instances ideal properties and coincidence theorems for the general classes are proved

volume estimates in spaces of homogeneous polynomials given m we derive upper and lower estimates for the volume of the unit ball of the banach space mathcal p m e n all m homogeneous polynomials defined on the nth section e n of a symmetric banach sequence space e with constants depending on m only we apply this result to obtain asymptotically correct orders of various important invariants of mathcal p m e n from local banach space theory as e g volume ratios cotype and type 2 constants projection constants or banach mazur distances

some applications of hypercontractive inequalities in quantum information theory hypercontractive inequalities have become important tools in theoretical computer science and have recently found applications in quantum computation in this note we discuss how hypercontractive inequalities in various settings can be used to obtain fairly concise proofs of several results in quantum information theory a recent lower bound of lancien and winter on the bias achievable by local measurements which are 4 designs spectral concentration bounds for k local hamiltonians and a recent result of pellegrino and seoane sepulveda giving general lower bounds on the classical bias obtainable in multiplayer xor games

the bohnenblust hille inequality for homogeneous polynomials is hypercontractive the bohnenblust hille inequality says that the 2m m 1 norm of the coefcients of an m homogeneous polynomial p on c n is bounded by kpk1 times a constant independent of n wherekk 1 denotes the supremum norm on the polydisc d n the main result of this paper is that this inequality is hypercontractive i e the constant can be taken to be c m for some c 1 combining this improved version of the bohnenblust hille inequality with other results we obtain the following the bohr radius for the polydisc d n behaves asymptotically as p logn n modulo a factor bounded away from 0 and innity

joint maximum a posteriori state path and parameter estimation in stochastic differential equations abstract in this article we introduce the joint maximum a posteriori state path and parameter estimator jme for continuous time systems described by stochastic differential equations sdes this estimator can be applied to nonlinear systems with discrete time sampled measurements with a wide range of measurement distributions we also show that the minimum energy state path and parameter estimator mee obtains the joint maximum a posteriori noise path initial conditions and parameters these estimators are demonstrated in simulated experiments in which they are compared to the prediction error method pem using the unscented kalman filter and smoother the experiments show that the mee is biased for the damping parameters of the drift function furthermore for robust estimation in the presence of outliers the jme attains lower state estimation errors than the pem

convergence of dirichlet polynomials in banach spaces both authors were supported by the mec project mtm2008 03211 the second author was partially supported by grants pr2007 0384 mec and upv paid 00 07

bohr radii of vector valued holomorphic functions abstract motivated by the scalar case we study bohr radii of the n dimensional polydisc d n for holomorphic functions defined on d n with values in banach spaces

on moduli spaces of sheaves on k3 or abelian surfaces we investigate the moduli spaces of one and two dimensional sheaves on projective k3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability we can exclude the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli spaces of one dimensional semistable sheaves on k3 surfaces and over components of many of the moduli spaces of two dimensional sheaves on k3 surfaces in particular of those for rank two sheaves

reverse inclusions for multiple summing operators abstract multiple summing operators have been proven to be useful in several areas of analysis and mathematical physics in this paper we prove reverse inclusions for this class of operators completing the work already initiated in d perez garcia the inclusion theorem for multiple summing operators studia math 165 3 2004 275 290

type and cotype of musielak orlicz sequence spaces let n be a musielak orlicz function and l the musielak orlicz sequence space generated by it is shown that satisfies condition qiff is equivalent to aq concave function n it is also proved thatl is of cotypeq typep if and only if satisfies condition q 2and pconditions respectively as applications we obtain characterization of the type and cotype of various sequence spaces nakano weighted orlicz and orlicz sequence spaces furthermore a relation betweenq concavity p convexity lowerq estimate upperp estimate and cotype type of l is given

some polynomial versions of cotype and applications abstract we introduce non linear versions of the classical cotype of banach spaces we show that spaces with l u st and cotype and spaces having fourier cotype enjoy our non linear cotype we apply these concepts to get results on convergence of vector valued power series in infinite many variables and on l 1 multipliers of vector valued dirichlet series finally we introduce cotype with respect to indexing sets an idea that includes our previous definitions