nilpotent gelfand pairs and spherical transforms of schwartz functions i rank one actions on the centre the spectrum of a gelfand pair of the form k ltimes n k where n is a nilpotent group can be embedded in a euclidean space mathbb r d the identification of the spherical transforms of k invariant schwartz functions on n with the restrictions to the spectrum of schwartz functions on mathbb r d has been proved already when n is a heisenberg group and in the case where n n3 2 is the free two step nilpotent lie group with three generators with k so3 astengo et al in j funct anal 251 772 791 2007 astengo et al in j funct anal 256 1565 1587 2009 fischer and ricci in ann inst fourier gren 59 2143 2168 2009 we prove that the same identification holds for all pairs in which the k orbits in the centre of n are spheres in the appendix we produce bases of k invariant polynomials on the lie algebra mathfrak n of n for all gelfand pairs k ltimes n k in vinberg s list vinberg in trans moscow math soc 64 47 80 2003 yakimova in transform groups 11 305 335 2006

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

on the cohen strongly p summing multilinear operators abstract in this paper we introduce and study a new concept of summability in the category of multilinear operators which is the cohen strongly p summing multilinear operators we prove a natural analog of the pietsch domination theorem and we compare the notion of p dominated multilinear operators with this class by generalizing a theorem of bu cohen

polynomial approximation in banach spaces abstract we define new classes of topological algebras of holomorphic functions on open subsets of banach spaces and on open subsets of dual banach spaces we investigate properties and derive results concerning polynomial approximation on such algebras we give an explicit description of their spectra derive results on finitely generated ideals and theorems of banach stone type we show that under certain conditions on the open subset u this new algebra coincides with h w u u deriving new results on h w u u

a new family of maximal curves over a finite field it has been known for a long time that the deligne lusztig curves associated to the algebraic groups of type 2a 2 2b 2 and 2g 2 defined over the finite field mathbb f n all have the maximum number of mathbb f n rational points allowed by the weil explicit formulas and that these curves are mathbb f q 2 maximal curves over infinitely many algebraic extensions mathbb f q 2 of mathbb f n serre showed that an mathbb f q 2 rational curve which is mathbb f q 2 covered by an mathbb f q 2 maximal curve is also mathbb f q 2 maximal this has posed the problem of the existence of mathbb f q 2 maximal curves other than the deligne lusztig curves and their mathbb f q 2 subcovers see for instance garcia on curves with many rational points over finite fields in finite fields with applications to coding theory cryptography and related areas pp 152 163 springer berlin 2002 and garcia and stichtenoth a maximal curve which is not a galois subcover of the hermitan curve bull braz math soc n s 37 139 152 2006 in this paper a positive answer to this problem is obtained for every q n 3 with n p r 2 p 2 prime we give a simple explicit construction of an mathbb f q 2 maximal curve mathcal x that is not mathbb f q 2 covered by any mathbb f q 2 maximal deligne lusztig curve furthermore the mathbb f q 2 automorphism group aut mathcal x has size n 3 n 3 1 n 2 1 n 2 n 1 interestingly mathcal x has a very large mathbb f q 2 automorphism group with respect to its genus g frac 1 2 n 3 1 n 2 2 1

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

strongly p summing multilinear operators abstract we define the concept of strongly p summing multilinear operators and prove that they have properly defined aron berner extensions some properties and examples are shown

the ramification sequence for a fixed point of an automorphism of a curve and the weierstrass gap sequence for nonsingular projective curves defined over algebraically closed fields of positive characteristic the dependence of the ramification filtration of decomposition groups of the automorphism group with weierstrass semigroups attached at wild ramification points is studied a faithful representation of the p part of the decomposition group at each wild ramified point to a riemann roch space is defined

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

automorphisms of harbater katz gabber curves let k be a perfect field of characteristic p 0 and let g be a finite group we consider the pointed g curves over k associated by harbater katz and gabber to faithful actions of g on k t over k we use such hkg g curves to classify the automorphisms of k t of p power order that can be expressed by particularly explicit formulas namely those mapping t to a power series lying in a mathbb z p mathbb z artin schreier extension of k t in addition we give necessary and sufficient criteria to decide when an hkg g curve with an action of a larger finite group j is also an hkg j curve

two lipschitz operator ideals abstract we introduce and investigate the concept of two lipschitz operator ideal between pointed metric spaces and banach spaces we show the basics of this new theory and we give a procedure to create a two lipschitz operator ideal from a linear operator ideal we apply our result to the ideals of strongly p summing and compact linear operator to obtain their corresponding two lipschitz operator ideal also we establish a natural relation between two lipschitz and bilinear maps and show that the two lipschitz factorable p dominated operators are those which are associated to the well known p semi integral bilinear operators

cyclic extensions and the local lifting problem the local oort conjecture states that if is cyclic and k is an algebraically closed eld of characteristic p then all extensions of k t should lift to characteristic zero we prove a critical case of this conjecture in particular we show that the conjecture is always true when vp j j 3 and is true for arbitrarily highly p divisible cyclic groups when a certain condition on the higher ramication ltration is satised

on gelfand pairs associated with solvable lie groups let g be a locally compact group and let k be a compact subgroup of aut g the group of automorphisms of g there is a natural action of k on the convolution algebra l g and we denote by lk g the subalgebra of those elements in l g that are invariant under this action the pair k g is called a gelfand pair if li g is commutative in this paper we consider the case where g is a connected simply connected solvable lie group and k c aut g is a compact connected group we characterize such gelfand pairs k g and determine a moduli space for the associated k spherical functions

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

an abstract result on cohen strongly summing operators abstract we present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of cohen strongly summing linear operators our argument is extended to multilinear operators and as a consequence we establish some alternative characterizations for the class of cohen strongly summing multilinear operators

entire functions on banach spaces with a separable dual abstract let e and f be complex banach spaces we show that if e has a separable dual then every holomorphic function from e into f which is bounded on weakly compact sets is bounded on bounded sets

entire functions on c0 abstract it is shown that every holomorphic function on c 0 which is bounded on weakly compact sets is bounded on bounded sets

abstract extrapolation theorems for absolutely summing nonlinear operators in this paper we prove a general version of the extrapolation theorem for absolutely summing nonlinear operators it is explicitly shown that this result encompasses the previous old and recent linear and nonlinear extrapolation theorems as particular cases one of the steps of the proof provides another nonlinear extrapolation theorem of independent interest

weak strong continuity of multilinear mappings and the pelczynski pitt theorem abstract in generalizing a result of pelczynski the sequential weak to norm continuity ofn linear mappings between certain banach spaces including spaces of type and cotype will be studied in particular it is shown that everyn linear continuous mapping from lp1 lpninto lqis compact if and only if i 1n 1 pi

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

derivative and factorization of holomorphic functions for a holomorphic function f of bounded type on a complex banach space e we show that its derivative df e e takes bounded sets into certain families of sets if and only if f may be factored in the form f g s where s is in some associated operator ideal and g is a holomorphic function of bounded type we also prove that the multilinear and polynomial mappings factor in an analogous way if and only if they are k bounded

quasi completely continuous multilinear operators we introduce the concept of quasi completely continuous multilinear operators and use this concept to characterize for a wide class of banach spaces x1 xk the multilinear operators t x1 xk x with an x valued aron berner extension

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

bases in the space of regular multilinear operators on banach lattices abstract for banach lattices e 1 e m and f with 1 unconditional bases we show that the monomial sequence forms a 1 unconditional basis of l r e 1 e m f the banach lattice of all regular m linear operators from e 1 e m to f if and only if each basis of e 1 e m is shrinking and every positive m linear operator from e 1 e m to f is weakly sequentially continuous as a consequence we obtain necessary and sufficient conditions for which the m fold fremlin projective tensor product e 1 e m resp the m fold positive injective tensor product e 1 e m has a shrinking basis or a boundedly complete basis

rolle s theorem for polynomials of degree four in a hilbert space in an infinite dimensional real hilbert space we introduce a class of fourth degree polynomials which do not satisfy rolle s theorem in the unit ball extending what happens in the finite dimensional case we show that every fourth degree polynomial defined by a compact operator satisfies rolle s theorem

the approximation property for spaces of holomorphic functions on infinite dimensional spaces ii let h u denote the vector space of all complex valued holomorphic functions on an open subset u of a banach space e let and respectively denote the compact ported topology and the bornological topology on h u we show that if e is a banach space with a shrinking schauder basis and with the property that every continuous polynomial on e is weakly continuous on bounded sets then h u and h u have the approximation property for every open subset u of e the classical space c0 the original tsirelson space t and the tsirelson james space tj are examples of banach spaces which satisfy the hypotheses of our main result our results are actually valid for riemann domains

spherical analysis on homogeneous vector bundles abstract given a lie group g a compact subgroup k and a representation k we assume that the algebra of end v valued bi equivariant integrable functions on g is commutative we present the basic facts of the related spherical analysis putting particular emphasis on the role of the algebra of g invariant differential operators on the homogeneous bundle e over g k in particular we observe that under the above assumptions g k is a gelfand pair and show that the gelfand spectrum for the triple g k admits homeomorphic embeddings in some c n in the second part we develop in greater detail the spherical analysis for g k h with h nilpotent in particular for h r n and k s o n and for h equal to the heisenberg group h n and k u n we characterize the representations k giving a commutative algebra

absolutely continuous multilinear operators abstract we introduce the new class of the p p 1 p m absolutely continuous multilinear operators that is defined using a summability property that provides the multilinear version of the p absolutely continuous operators we give an analogue of the pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for p absolutely continuous operators obtaining in this way a rich factorization theory we present also a tensor norm which represents this multi ideal by trace duality as an application we show that p p 1 p m absolutely continuous multilinear operators are compact under some requirements applications to factorization of linear maps on banach function spaces through interpolation spaces are also given

large p group actions with a p elementary abelian derived group let k be an algebraically closed field of characteristic p 0 and c a connected nonsingular projective curve over k with genus g 2 let c g be a big action i e a pair c g where g is a p subgroup of the k automorphism group of c such that g g 2pp 1 the aim of this paper is to describe the big actions whose derived group g is p elementary abelian in particular we obtain a structure theorem for the functions parametrizing the artin schreier cover c c g using artin schreier duality we shift to a group theoretic point of view to characterize relevant cases then we display universal families and discuss the corresponding deformation space for p 5

cohomology of g sheaves in positive characteristic let g be a finite group and x a noetherian g scheme defined on an algebraically closed field k whose characteristic divides the order of g we define a refinement of the equivariant k theory of x devoted to give a better account of the information related to modular representation theory the construction relies in an essential way on the work of m auslander in modular representation theory and the use of sheaves of rings with several objects the main applications of this modular k theory are in dimension one where we show how it allows to extend the work of s nakajima

factorization of holomorphic mappings in infinite dimensions this note is concerned with a generalization of the first identity to the non linear setting of holomorphic i e complex analytic functions on e in fact our interest in this generalization arose from a study made by the second author 15 of a suitable generalization of the second identity to the holomorphic setting however our results and methods have little in common with 15 in somewhat simplistic terms our results provide further evidence that in many situations one is justified in regarding the space h e of holomorphic functions on e as the holomorphic dual of e which shares many properties with the standard linear dual of e see for example 6 a brief outline of this paper follows after which we recall some basic results about holomorphic mappings between infinite dimensional locally convex spaces in section 2 we investigate when a holomorphic function f u c on a balanced open subset u of e admits a factorization through u a characterization of factorizable functions is given in terms of the derivative o f f our basic technique is

deformations formelles des revetements sauvagement ramifies de courbes algebriques in this paper we study formal moduli for wildly ramified galois covering we prove a local global principle we then focus on the infinitesimal deformations of the z pz covers we explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p 2 by deforming artin schreier equations we obtain a lower bound on the dimension of the local versal deformation ring at last by comparing the global versal deformation ring to the complete local ring in a point of a moduli space we determine the dimensions of the global and local versal deformation rings

analytic approximations of uniformly continuous functions in real banach spaces abstract it is shown that if a separable real banach space x admits a separating analytic function with an additional condition property k concerning uniform behaviour of radii of convergence then every uniformly continuous mapping on x into any real banach space y can be approximated by analytic operators in particular the result applies to c0

weakly continuous holomorphic functions on banach spaces with a shrinking and unconditional basis let e and f be complex banach spaces and let u be an open ball in e we show that if e has a shrinking and unconditional basis then every holomorphic function f u f that is weakly continuous on u bounded sets is weakly uniformly continuous on u bounded sets

weakly sequentially continuous differentiable mappings abstract it is well known that a linear operator t l x y between banach spaces is completely continuous if and only if its adjoint t l y x takes bounded subsets of y into uniformly completely continuous subsets often called l subsets of x we give similar results for differentiable mappings more precisely if u x is an open convex subset let f u y be a differentiable mapping whose derivative f u l x y is uniformly continuous on u bounded subsets we prove that f takes weak cauchy u bounded sequences into convergent sequences if and only if f takes rosenthal u bounded subsets of u into uniformly completely continuous subsets of l x y as a consequence we extend a result of p hajek and answer a question raised by r deville and e matheron we derive differentiable characterizations of banach spaces not containing l 1 and of banach spaces without the schur property containing a copy of l 1 analogous results are given for differentiable mappings taking weakly convergent u bounded sequences into convergent sequences finally we show that if x has the hereditary dunford pettis property then every differentiable function f u r as above is locally weakly sequentially continuous

extensions of smooth mappings into biduals and weak continuity abstract we study properties of uniformly differentiable mappings between real banach spaces among our main results are generalizations of a number of classical results for linear operators on l spaces into the setting of uniformly differentiable mappings denote by b x the closed unit ball of a banach space x let x be a l space 1 and let y be a banach space let t b x y be a continuous mapping which is uniformly differentiable in the open unit ball of x assuming that t is weakly compact then t can be extended preserving its best smoothness properties into the mapping from the 1 multiple of the unit ball of any superspace of the domain space x into the same range space y we also show that t maps weakly cauchy sequences from b x into norm convergent sequences in y this is a uniformly smooth version of the dunford pettis property for the l spaces we also show that a uniformly differentiable mapping t which is not necessarily weakly compact still maps weakly cauchy sequences from b x into norm convergent sequences in y provided y does not contain an isomorphic copy of c 0 we prove that for certain pairs of banach spaces the completion of the space of polynomials equipped with the topology of uniform convergence on the bounded sets of the functions and their derivatives up to order k coincides with the space of uniformly differentiable up to order k mappings our work is based on a number of tools that are of independent interest we prove for every pair of banach spaces x y that any continuous mapping t b x y which is uniformly differentiable of order up to k in the interior of b x can be extended preserving its best smoothness into a bidual mapping t b x y another main tool is a result of zippin s type we show that weakly cauchy sequences in x c k can be uniformly well approximated by weakly cauchy sequences from a certain c 0 is a countable ordinal subspace of x

polynomial algebras and smooth functions in banach spaces abstract let a n x be the algebra of polynomials on a real banach space x which is generated by all continuous polynomials of degree not exceeding n let m be the minimal integer such that there is a non compact m homogeneous polynomial p p x m l 1 then n m implies that the uniform closure of a n x does not contain all polynomials of degree n 1 and hence the chain of closures a n x n m is strictly increasing in the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on banach spaces posed in the literature in particular we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain banach space x such that there exists no uniformly differentiable function g on b x for any 1 which coincides with f in some neighbourhood of the origin

algebraic curves with a large non tame automorphism group fixing no point let k be an algebraically closed field of characteristic p 0 and let x be a curve over k of genus g 2 assume that the automorphism group aut x of x over k fixes no point of x the following result is proven if there is a point p on x whose stabilizer in aut x contains a p subgroup of order greater than gp p 1 then x is birationally equivalent over k to one of the irreducible plane curves ii iii iv v listed in the introduction

polynomial properties of banach spaces abstract several properties defined by polynomials on a banach space are introduced and briefly studied we apply them to give necessary and sufficient conditions for the non containment of l 1 in a symmetric projective tensor product of banach spaces

a cohomological treatise of hkg covers with applications to the nottingham group abstract we characterize harbater katz gabber curves in terms of a family of cohomology classes satisfying a compatibility condition our construction is applied to the description of finite subgroups of the nottingham group

multilinear variants of maurey and pietsch theorems and applications we prove composition results for multilinear operators and multilinear variants of maurey and pietsch theorems both for multiple p summing p dominated and p summing multilinear operators

asymptotic structure lp estimates of sequences and compactness of multilinear mappings abstract we relate the moduli of asymptotic uniform smoothness and convexity of a banach space with the existence of upper and lower l p estimates of sequences in the space to this end we introduce two properties which are related to the m p property defined by kalton and werner in this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity and compactness or weak sequential continuity of multilinear mappings finally we give some applications to the existence of analytic and asymptotically flat norms on a banach space

polynomial sequential continuity on c k e spaces we show that for bounded sequences in c k e the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence we introduce several conditions on e under which different versions of the result are true when k is a scattered compact space these conditions are related with some others appeared in the literature and they seem to be of independent interest

p ranks and automorphism groups of algebraic curves let x be an irreducible complete nonsingular curve of genus g over an algebraically closed field k of positive characteristic p if 9 2 the automorphism group aut x of x is known to be a finite group and moreover its order is bounded from above by a polynomial in g of degree four stichtenoth in this paper we consider the frank zy of x and investigate relations between zy and aut x we show that zy affects the order of a sylow psubgroup of aut x 3 and that an inequality iaut x 84 9 1 9 holds for an ordinary i e zy g curve x 4

factorization of injective ideals by interpolation we construct a factorization of certain multilinear mappings through linear operators belonging to closed injective operator ideals using interpolation technique an extension of the duality theorem for interpolation spaces is also obtained

on cohen almost summing multilinear operators abstract we show that all cohen strongly p summing multilinear operators and polynomials on banach spaces are cohen almost summing if the range space is a hilbert space then all cohen strongly p summing multilinear operators and polynomials are strongly q summing 1 p q moreover if both domain and range spaces are hilbert spaces then all hilbert schmidt multilinear operators are cohen strongly 2 summing

weak sequential completeness of spaces of homogeneous polynomials abstract let p w e n f be the space of all continuous n homogeneous polynomials from a banach space e into another f that are weakly continuous on bounded sets we give sufficient conditions for the weak sequential completeness of p w e n f these sufficient conditions are also necessary if both e and f have the bounded compact approximation property we also show that the weak sequential completeness and the reflexivity of p w e n f are equivalent whenever both e and f are reflexive

duality in spaces of nuclear and integral polynomials abstract we study the spaces of nuclear and integral vector valued polynomials and their duals we prove that if e is asplund p n ne f p i ne f isometrically for any banach space f we describe p n ne f as a subspace of p ne f in terms of weak star continuous polynomials we show that p w ne f p c ne f when e has the approximation property

the oort conjecture on lifting covers of curves we show that the conjecture of oort on lifting covers of curves is true the main ingredients in the proof are a deformation argument in characteristic p and a special case of a very recent result by obus wewers a kind of boundedness result is given as well