gaudin models with irregular singularities abstract we introduce a class of quantum integrable systems generalizing the gaudin model the corresponding algebras of quantum hamiltonians are obtained as quotients of the center of the enveloping algebra of an affine kac moody algebra at the critical level extending the construction of higher gaudin hamiltonians from b feigin et al 1994 17 to the case of non highest weight representations of affine algebras we show that these algebras are isomorphic to algebras of functions on the spaces of opers on p 1 with regular as well as irregular singularities at finitely many points we construct eigenvectors of these hamiltonians using wakimoto modules of critical level and show that their spectra on finite dimensional representations are given by opers with trivial monodromy we also comment on the connection between the generalized gaudin models and the geometric langlands correspondence with ramification

noisy fir identification as a quadratic eigenvalue problem this correspondence describes a method for identifying fir models in the presence of input and output noise the proposed algorithm takes advantage of both the bias compensation principle and the instrumental variable method it is based on a nonlinear system of equations whose unknowns are the fir coefficients and the input noise variance this system allows mapping the noisy fir identification problem into a quadratic eigenvalue problem the identification problem is thus solved without requiring the use of iterative least squares algorithms the performance of the proposed approach has been tested and compared with that of other identification methods by means of monte carlo simulations

tensor product of n isometries abstract a hilbert space operator a is an m isometry if k 0 m 1 k m k a m k a m k 0 we prove that the tensor product of an m isometry a with an n isometry b is an m n 1 isometry this proves a conjecture of botelho and jamison 5 remark 5 1

optimized estimation of moments for nonstationary signals the behavior of nonstationary moment estimators that are based on linear time invariant filtering is analyzed the performance of such estimators is evaluated in terms of their time averaged variance and time averaged squared bias optimal estimators that minimize a convex combination of bias and variance are derived the superiority of such optimally weighted filtering over the conventional exponentially windowed moment estimation technique is demonstrated by means of a simple example the same example also serves to illustrate the difficulties encountered when the construction of optimal estimators relies on uncertain prior information as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed robust optimal estimators we also include a brief discussion of the relevance of the proposed moment estimation technique to identification of linear time variant systems and to estimation of time variant spectra

dual h _ infty algorithms for signal processing application to speech enhancement this paper deals with the joint signal and parameter estimation for linear state space models an efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual kalman filters in that case the driving process and the observation noise in the state space representation for each filter must be white with known variances these conditions however are too strong to be always satisfied in real cases to relax them we propose a new approach based on two dual hinfin filters once a new observation of the disturbed signal is available the first hinfin algorithm uses the latest estimated parameters to estimate the signal while the second hinfin algorithm uses the estimated signal to update the parameters in addition as the hinfin filter behavior depends on the choice of various weights we present a way to recursively tune them this approach is then studied in the following cases 1 consistent estimation of the ar parameters from noisy observations and 2 speech enhancement where no a priori model of the additive noise is required for the proposed approach in each case a comparative study with existing methods is carried out to analyze the relevance of our solution

dirichlet type spaces on the unit ball and joint 2 isometries abstract we obtain a formula that relates the spherical moments of the multiplication tuple on a dirichlet type space to a complex moment problem in several variables this can be seen as the ball analogue of a formula originally invented by richter in 23 we capitalize on this formula to study dirichlet type spaces on the unit ball and joint 2 isometries

deformations of galois representations and exceptional monodromy for any simple algebraic group g of exceptional type we construct geometric ell adic galois representations with algebraic monodromy group equal to g in particular producing the first such examples in types mathrm f 4 and mathrm e 6 to do this we extend to general reductive groups ravi ramakrishna s techniques for lifting odd two dimensional galois representations to geometric ell adic representations

linear differential equations and multiple zeta values iii zeta 3 we consider the hypergeometric equation 1 t t t g x3g 0 whose unique analytic solution 1 t x 1 o t near t 0 for t 1 becomes a generating function for multiple zeta values 1 1 x f3 x 1 3 x3 3 3 x6 we apply the so called wkb method to study solutions of the hypergeometric equation for large x and we calculate corresponding stokes matrices we prove that the function f3 x near x is also expressed via wkb type functions which subject to some stokes phenomenon this implies that f3 x satisfies a sixth order linear differential equation with irregular singularity at infinity

a geometric analogue of a conjecture of gross and reeder let g be a simple complex algebraic group we prove that the irregularity of the adjoint connection of an irregular flat g bundle on the formal punctured disk is always greater than or equal to the rank of g this can be considered as a geometric analogue of a conjecture of gross and reeder we will also show that the irregular connections with minimum adjoint irregularity are precisely the formal frenkel gross connections as a corollary we establish the de rham analogue of a conjecture of heinloth ngo and yun for g sln

an example of the langlands correspondence for irregular rank two connections on p1 abstract special kinds of rank 2 vector bundles with possibly irregular connections on p 1 are considered we construct an equivalence between the derived category of quasi coherent sheaves on the moduli stack of such bundles and the derived category of modules over a tdo ring on certain non separated curve we identify this curve with the coarse moduli space of some parabolic bundles on p 1 then our equivalence becomes an example of the categorical langlands correspondence

a representation theorem for cyclic analytic two isometries a bounded linear operator t on a complex separable hilbert space z is called a 2 isometry if t 2t2 2t t i o we say that t is analytic if nn 0 tnt 0 in this paper we show that every cyclic analytic 2 isometry can be represented as multiplication by z on a dirichlet type space d 8 here ze denotes a finite positive borel measure on the unit circle for two measures u and v the 2 isometries obtained as multiplication by z on d 8 and d v are unitarily equivalent if and only if u v we also investigate similarity and quasisimilarity of these 2 isometries and we apply our results to the invariant subspaces of the dirichlet shift

opers for higher states of quantum kdv models we study the ode im correspondence for all states of the quantum widehat mathfrak g kdv model where widehat mathfrak g is the affinization of a simply laced simple lie algebra mathfrak g we construct quantum widehat mathfrak g kdv opers as an explicit realization of the class of opers introduced by feigin and frenkel exploring new structures and natural constructions in mathematical physics math soc japan tokyo 2011 which are defined by fixing the singularity structure at 0 and infty and by allowing a finite number of additional singular terms with trivial monodromy we prove that the generalized monodromy data of the quantum widehat mathfrak g kdv opers satisfy the bethe ansatz equations of the quantum widehat mathfrak g kdv model the trivial monodromy conditions are equivalent to a complete system of algebraic equations for the additional singularities

non integrability by discrete quadratures we give a necessary condition for integrability by discrete quadratures of systems of difference equations the discrete variational equations along algebraic solutions must have virtually solvable galois groups this necessary condition a la morales and ramis is used in order to prove that q analogues of painleve i and painleve iii equations are not integrable by discrete quadratures

m isometric operators and their local properties abstract in this paper we give necessary and sufficient conditions for a bounded linear hilbert space operator to be an m isometry for an unspecified m written in terms of conditions that are applied to one vector at a time we provide criteria for orthogonality of generalized eigenvectors of an a priori unbounded linear operator t on an inner product space that correspond to distinct eigenvalues of modulus 1 we also discuss a similar question of when jordan blocks of t corresponding to distinct eigenvalues of modulus 1 are orthogonal

decomposing algebraic m isometric tuples abstract we show that any m isometric tuple of commuting algebraic operators on a hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple our approach applies as well to tuples of algebraic operators that are hereditary roots of polynomials in several variables

irreducible cuspidal representations with prescribed local behavior let g be a simple algebraic group defined over the global field k in this paper we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of g with specified local behavior at a finite set of places of k and unramified elsewhere this sum is expressed as the product of the values of modified artin l functions at negative integers

on m p expansive and m p contractive operators on hilbert and banach spaces for a bounded operator t on a banach space x we define m p t x k 0m 1 m k mk tkx pfor all x x we prove m p t x 0 for all x x implies m 1 p t x 0 for all x x this result allows us to extend several results for m p isometries m p t x 0 to operators only satisfying m p t x 0 a berger shaw type result is also proved for a class of m expansive operators on a hilbert space several classes of operators are introduced and studied by using m p t x in parallel with corresponding classes of operators on hilbert space in particular a class of p subnormal operators on a banach space is introduced and such operators are proved to be paranormal

a solution to the cauchy dual subnormality problem for 2 isometries abstract the cauchy dual subnormality problem asks whether the cauchy dual operator t t t t 1 of a 2 isometry t is subnormal in the present paper we show that the problem has a negative solution the first counterexample depends heavily on a reconstruction theorem stating that if t is a 2 isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition then t is subnormal if and only if t satisfies the unperturbed kernel condition the second counterexample arises from a 2 isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the cauchy dual subnormality problem in this context we prove that if t is a 2 isometry satisfying the kernel condition or a quasi brownian isometry then t is subnormal we construct a 2 isometric adjacency operator t of a rooted directed tree such that t does not satisfy the kernel condition t is not a quasi brownian isometry and t is subnormal

strict isometries of arbitrary orders abstract we consider the elementary operator l acting on the hilbert schmidt class c 2 h given by l t atb with a and b bounded operators on a separable hilbert space h in this paper we establish results relating isometric properties of l with those of the defining symbols a and b we also show that if a is a strict n isometry on a hilbert space h then i a a a 2 a 2 a n 1 a n 1 is a linearly independent set of operators this result allows to extend further the isometric interdependence of l and its symbols in particular we show that if l is a p isometry then a is a strict p 1 or p 2 isometry if and only if b is a strict 2 or 3 isometry

speech enhancement combining optimal smoothing and errors in variables identification of noisy ar processes in the framework of speech enhancement several parametric approaches based on an a priori model for a speech signal have been proposed when using an autoregressive ar model three issues must be addressed 1 how to deal with ar parameter estimation indeed due to additive noise the standard least squares criterion leads to biased estimates of ar parameters 2 can an estimation of the variance of the additive noise for each speech frame be obtained a voice activity detector is often used for its estimation 3 which estimation rules and techniques filtering smoothing etc can be considered to retrieve the speech signal our contribution in this paper is threefold first we propose to view the identification of the noisy ar process as an errors in variables problem this blind method has the advantage of providing accurate estimations of both the ar parameters and the variance of the additive noise second we propose an alternative algorithm to standard kalman smoothing based on a constrained minimum variance estimation procedure with a lower computational cost third the combination of these two steps is investigated it provides better results than some existing speech enhancement approaches in terms of signal to noise ratio snr segmental snr and informal subjective tests

a m isometries on hilbert spaces abstract a bounded linear operator t on a hilbert space h is called an a m isometry for some positive operator a on h and integer m if k 0 m 1 m k m k t k a t k 0 we give some properties of a m isometries in particular we focus on spectral properties and the relation between a m isometries and m isometries also we obtain some dynamic properties of a m isometries as a negative answer to 22 question 1 with an example of an a isometric which is n supercyclic and sufficient conditions for an a m isometry to be not n supercyclic moreover we prove that the perturbation of a m isometry by a bigger class than nilpotent operators is not n supercyclic

elementary properties of isometries on a hilbert space inspired by recent works on m isometries for a positive integer m in this paper we introduce the classes of isometries and unitaries on a hilbert space we show that an isometry on a finite dimensional complex hilbert space h with dimension n is in fact an 2n 1 isometry we describe the spectra of such operators study the quasinilpotent perturbations of isometries and characterize when tensor products of isometries are also isometries as a surprising by product we obtain a generalization of nagy foias langer decomposition of a contraction into an unitary and a completely nonunitary contraction

connected linear groups as differential galois groups theorem 1 1 let c be an algebraically closed field of characteristic zero g a connected linear algebraic group defined o er c and k a differential field containing c as its field of constants and of finite nonzero transcendence degree o er c then g can be realized as the galois group of a picard vessiot extension of k w x previous work by kovacic 17 18 reduced this problem to the case of powers of a simple connected linear algebraic group our contribution is to show that one is able to realize any connected semisimple group as a galois group and when k s c x x9 s 1 to control the number and types of singularities when one constructs a system y 9 s ay a g m c x realizing an arbitrary connected linear algebraic group as its n

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

on the noise compensated yule walker equations recently a method of estimating the parameters of an ar p random process based on measurements corrupted by additive white noise was described the method involves solving a matrix pencil called the noise compensated yule walker ncyw equations for the ar parameters and the variance of the measurement noise we give a necessary and sufficient condition for there to exist a unique solution to the ncyw equations

differential tannakian categories abstract we define a differential tannakian category and show that under a natural assumption it has a fibre functor if in addition this category is neutral that is the target category for the fibre functor are finite dimensional vector spaces over the base field then it is equivalent to the category of representations of a pro linear differential algebraic group our treatment of the problem is via differential hopf algebras and deligne s fibre functor construction p deligne categories tannakiennes in the grothendieck festschrift vol ii in progr math vol 87 birkhauser boston boston ma 1990 pp 111 195

opers with irregular singularity and spectra of the shift of argument subalgebra joint work with boris feigin and edward frenkel math qa 0712 1183 let g be a semisimple complex lie algebra and u g its universal enveloping algebra the algebra u g bears a natural filtration by the degree with respect to the generators the associated graded algebra is the symmetric algebra s g c g by the poincare birkhoff witt theorem the commutator on u g defines the poisson bracket on s g let zs g s g be the center of s g with respect to the poisson bracket and let g g be a regular semisimple element due to the result of mischenko and fomenko 1978 the algebra a s g generated by the elements where zs g is commutative with respect to the poisson bracket and has maximal possible transcendence degree equal to 12 dim g rk g if is a regular element contained in the cartan subalgebra h g then h a and if f is the principal nilpotent element then the subalgebra af contains the principal nilpotent subalgebra zg f it was recently shown that the shift of argument subalgebras can be quantized

novel parameter estimation of autoregressive signals in the presence of noise this paper proposes a new method for estimating the parameters of an autoregressive ar signal from observations corrupted by white noise the feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the ar parameters moreover a convergent newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method as a result the proposed new method can minimize the error of estimating the variance of the observation noise since more accurate estimates of this observation noise variance can be attained at earlier stages the proposed method can achieve a good performance in estimating the ar signal parameters numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms

an isometry plus a nilpotent operator is an m isometry applications abstract we prove that if an isometry a and a nilpotent operator q of order n commute then a q is a strict 2 n 1 isometry as an application of the main result we prove that a q cannot be n supercyclic for any n also we find an m isometry with prescribed spectrum k where k is the closed unit disk or a compact subset of the unit circle

estimation of all pole model parameters from noise corrupted sequences least squares estimates of the parameters of all pole signal models are biased when applied to noise corrupted all pole sequences this bias has been shown to be proportional to the inverse of the signal to noise ratio an autocorrelation like procedure is shown to increase under some circumstances the signal to noise ratio while retaining the pole locations when the noise is white the signal to noise ratio improvement varies for each mode in the all pole sequence with modes corresponding to pole locations close to the unit circle showing the most improvement a signal to noise ratio cutoff exists for each mode below which no improvement can be obtained this cutoff depends on the proximity of the pole location to the unit circle approaching zero as the pole nears the origin this cutoff corresponds to the point at which a mode s spectral value just equals the level of the noise floor this procedure can be applied recursively until an acceptable signal to noise ratio is obtained the all pole parameters can then be estimated from the processed sequence using least squares estimation

classification of hereditary matrices abstract a classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices t such that p t 0 we consider matrices and operators which satisfy a different type of polynomial constraint let h be a complex hilbert space t be a bounded linear transformation of h t be the adjoint of t and c x y be the algebra of polynomials in x and y with complex coefficients for a polynomial p c x y in two variables with complex coefficients define p t m n 0 p m n t n t m where p m n is the coefficient of ynxm in the expansion of p in a power series about the point 0 0 t is called a root of p if and only if p t 0 note that if p c x y is a polynomial in the single variable x then the definition of p t given here agrees with the classical definition in this paper we study the relationships which p t 0 forces between p and t when t is an algebraic operator i e there exists n 1 and complex numbers a0 an 1 such that 0 a0 a1t an 1tn 1 tn the classification starts with the following observation suppose p c x y and an algebraic operator t l h satisfy p t 0 then certain subspaces of h which are invariant for t must be orthogonal or certain coefficients of p must vanish this leads to the notions of a graph attached to each p c x y and a graph attached to each square matrix t for diagonalizable t a necessary and sufficient graph theoretic condition for solving p t 0 is given for nondiagonalizable t this condition is necessary but not sufficient the use of these graphs does however reduce the problem to the problem of solving the equation p t 0 for t with exactly one or two eigenvalues for t with one eigenvalue we give a necessary and sufficient condition for solving p t 0 this leaves the case of solving p t 0 when t has exactly two eigenvalues this problem mixes algebra involving polynomials with matrix theory we show that it is equivalent to the purely algebraic problem of determining if equations of the form i j eci jxi r j s 0 have solutions of finite support with certain nonvanishing properties we call these equations bi hankel equations subordinate to a given subset e of the lattice of integer pairs i j 0 i m 1 0 j n 1 it turns out that there is an algorithm which uses grobner bases for determining if the type of solution we seek exists and for computing it

algebraic properties of operator roots of polynomials abstract properties of m selfadjoint and m isometric operators have been investigated by several researchers particularly interesting to us are algebraic properties of nilpotent perturbations of such operators mccullough and rodman showed in the nineties that if q n 0 and a is a selfadjoint operator commuting with q then the sum a q is a 2 n 1 selfadjoint operator very recently bermudez martinon and noda proved a similar result for nilpotent perturbations of isometries via a new approach we obtain simple proofs of these results and other generalizations to operator roots of polynomials

3 d ar model order selection via rank test procedure this paper deals with the problem of three dimensional autoregressive 3 d ar model order estimation we show that the information for the 3 d ar model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function acf of the underlying 3 d gaussian process exploiting this property we develop an algorithm to estimate the order p1 p2 p3 corresponding to the quarter space qs region of support the proposed method is based upon a rank test procedure rtp using singular value decomposition svd and solving nonlinear system equations numerical simulations are presented to illustrate the performances of the proposed algorithm

a rigid irregular connection on the projective line in this paper we construct a connection on the trivial g bundle on p 1 for any simple complex algebraic group g which is regular outside of the points 0 and has a regular singularity at the point 0 with principal unipotent monodromy and has an irregular singularity at the point with slope 1 h the reciprocal of the coxeter number of g the connection which admits the structure of an oper in the sense of beilinson and drinfeld appears to be the characteristic 0 counterpart of a hypothetical family of l adic representations which should parametrize a specific automorphic representation under the global langlands correspondence these l adic representations and their characteristic 0 counterparts have been constructed in some cases by deligne and katz our connection is constructed uniformly for any simple algebraic group and characterized using the formalism of opers it provides an example of the geometric langlands correspondence with wild ramification we compute the de rham cohomology of our connection with values in a representation v of g and describe the differential galois group of as a subgroup of g

some results on higher order isometries and symmetries products and sums with a nilpotent operator abstract we study the sum of an m isometry or an m symmetric operator with a nilpotent operator we also study the product of two m isometries or two n symmetries we obtain several theorems generalizing previous work our method is straightforward and thus offers direct and simple insights into why these theorems are true

a subspace approach to estimation of autoregressive parameters from noisy measurements this correspondence describes a method for estimating the parameters of an autoregressive ar process from a finite number of noisy measurements the method uses a modified set of yule walker yw equations that lead to a quadratic eigenvalue problem that when solved gives estimates of the ar parameters and the measurement noise variance

stokes matrices poisson lie groups and frobenius manifolds the purpose of this paper is to point out and then draw some consequences of the fact that the poisson lie group g dual to g gln c may be identified with a certain moduli space of meromorphic connections over the unit disc having an irregular singularity at the origin g will be fully described in sect 2 the key feature of this point of view is that there is a holomorphic map g g from the dual of the lie algebra to the group g for each choice of diagonal matrix a0 with distinct eigenvalues the irregular type this map is essentially the riemann hilbert map or de rham morphism for such connections we will call it the monodromy map it is generically a local analytic isomorphism the main result is

compatibility of the feigin frenkel isomorphism and the harish chandra isomorphism for jet algebras let g be a simple finite dimensional complex lie algebra with a cartan subalgebra h and weyl group w let g denote the lie algebra of n jets on g a theorem of rais and tauvel and geoffriau identifies the centre of the category of g modules with the algebra of functions on the variety of n jets on the affine space h w on the other hand a theorem of feigin and frenkel identifies the centre of the category of critical level smooth modules of the corresponding affine kac moody algebra with the algebra of functions on the ind scheme of opers for the langlands dual group we prove that these two isomorphisms are compatible by defining the higher residue of opers with irregular singularities we also define generalized verma and wakimoto modules and relate them by a nontrivial morphism

motives with exceptional galois groups and the inverse galois problem we construct motivic l adic representations of textup gal overline mathbb q mathbb q into exceptional groups of type e 7 e 8 and g 2 whose image is zariski dense this answers a question of serre the construction is uniform for these groups and is inspired by the langlands correspondence for function fields as an application we solve new cases of the inverse galois problem the finite simple groups e 8 mathbb f ell are galois groups over mathbb q for large enough primes l

on the algebraic relations between mahler functions in the last years a number of authors have studied the algebraic relations between the generating series of automatic sequences it turns out that these series are solutions of mahler type equations this paper is mainly concerned with the difference galois groups of mahler type equations these groups reflect the algebraic relations between the solutions of the equations in particular we study in details the equations of order 2 and compute the difference galois groups of classical equations related to the baum sweet and to the rudin shapiro automatic sequences

elementary operators which are m isometries abstract the study of m isometry elementary operator of length one is initiated by botelho and jamison several authors have contributed to obtain this result if the two operator coefficients involved are m isometries then the elementary operator is m isometry on the hilbert schmidt operator ideal in this paper we show that the converse of this result is also true we also give a necessary and sufficient condition for the generalized derivation to be an m isometry the sufficiency follows from results on the sum of m isometries and nilpotent operators in two recent papers

products of m isometries abstract an operator t on a banach space x is called an m p isometry if it satisfies the equality k 0 m m k 1 m k t k x p 0 for all x x in this paper we prove that if t is an n p isometry s is an m p isometry and they commute then ts is an m n 1 p isometry this result applied to elementary operators of length 1 defined on the hilbert schmidt class proves a conjecture in 11

galois theory for iterative connections and nonreduced galois groups this article presents a theory of modules with iterative connection this theory is a generalisation of the theory of modules with connection in characteristic zero as given by n katz to modules over rings of arbitrary characteristic we show that these modules with iterative connection and also the modules with integrable iterative connection form a tannakian category assuming some nice properties for the underlying ring and we show how this generalises to modules over schemes stratifications on modules as introduced by a grothendieck generalise the notion of integrable ordinary connections in another way however over smooth rings we obtain an equivalence of stratifications and integrable iterative connections furthermore over a regular ring in positive characteristic we show that the category of modules with integrable iterative connection is also equivalent to the category of flat bundles as defined by d gieseker in the second part of this article we set up a picard vessiot theory for fields of solutions for such a picard vessiot extension we obtain a galois correspondence which takes into account even nonreduced closed subgroup schemes of the galois group scheme on one hand and inseparable intermediate extensions of the picard vessiot extension on the other hand finally we compare our galois theory with the galois theory for purely inseparable field extensions given by s chase

preservation of depth in the local geometric langlands correspondence it is expected that under mild conditions the local langlands correspondence preserves depths of representations in this article we formulate a conjectural geometrisation of this expectation we prove half of this conjecture by showing that the depth of a categorical representation of the loop group is greater than or equal to the depth of its underlying geometric langlands parameter a key ingredient of our proof is a new definition of the slope of a meromorphic connection a definition which uses opers

kloosterman sheaves for reductive groups deligne constructed a remarkable local system on p 1 f 0 1g attached to a family of kloosterman sums katz calculated its monodromy and asked whether there are kloosterman sheaves for general reductive groups and which automorphic forms should be attached to these local systems under the langlands correspondence motivated by work of gross and frenkel gross we nd an explicit family of such automorphic forms and even a simple family of automorphic sheaves in the framework of the geometric langlands program we use these automorphic sheaves to construct adic kloosterman sheaves for any reductive group in a uniform way and describe the local and global monodromy of these kloosterman sheaves in particular they give motivic galois representations with exceptional monodromy groups g2 f4 e7 and e8 this also gives an example of the geometric langlands correspondence with wild ramication for any reductive group

packets in grothendieck s section conjecture abstract the goal of this article is to show a part of grothendieck s section conjecture using the identification of sections with neutral fiber functors as defined in h esnault p h hai the fundamental groupoid scheme and applications preprint 2006 34 pp

on convex cyclic operators abstract we give a hahn banach characterization for convex cyclicity we also obtain an example of a bounded linear operator s on a banach space with p s such that s is convex cyclic but s is not weakly hypercyclic and s 2 is not convex cyclic this solved two questions of rezaei in 25 when p s we also characterize the diagonalizable normal operators that are convex cyclic and give a condition on the eigenvalues of an arbitrary operator for it to be convex cyclic we show that certain adjoint multiplication operators are convex cyclic and show that some are convex cyclic but no convex polynomial of the operator is hypercyclic also some adjoint multiplication operators are convex cyclic but not 1 weakly hypercyclic

frequency domain identification of fir models in the presence of additive input output noise this paper describes a new approach for identifying fir models from a finite number of measurements in the presence of additive and uncorrelated white noise in particular two different frequency

ergodic and dynamical properties of m isometries abstract an example of a weakly ergodic 3 isometry is provided in 3 we give new examples of weakly ergodic 3 isometries and study numerically hypercyclic m isometries on finite and infinite dimensional hilbert spaces in particular all weakly ergodic strict 3 isometries on a hilbert space are weakly numerically hypercyclic adjoints of unilateral forward weighted shifts which are strict m isometries on l 2 n are shown to be hypercyclic

canonical decomposition of irreducible linear differential operators with symplectic or orthogonal differential galois groups we first revisit an order six linear differential operator already introduced in a previous paper having a solution which is a diagonal of a rational function of three variables this linear differential operator is such that its exterior square has a rational solution indicating that it has a selected differential galois group and is actually homomorphic to its adjoint we obtain the two corresponding intertwiners giving this homomorphism to the adjoint we show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition already underlined in a previous paper in terms of order two self adjoint operators from these results we deduce a new form of decomposition of operators for this selected order six linear differential operator in terms of three order two self adjoint operators we generalize this decomposition to decomposition in terms of three self adjoint operators of arbitrary orders provided the three orders have the same parity we then generalize the previous decomposition to decompositions in terms of an arbitrary number of self adjoint operators of the same parity order this yields an infinite family of linear differential operators homomorphic to their adjoint and thus with a selected differential galois group we show that the equivalence of such operators with selected differential galois groups is compatible with these canonical decompositions the rational solutions of the symmetric or exterior squares of these selected operators are noticeably seen to depend only on the rightmost self adjoint operator in the decomposition these results and tools are applied on operators of large orders for instance it is seen that a large set of quite massive operators associated with reflexive 4 polytopes defining calabi yau three folds obtained recently by lairez correspond to a particular form of the decomposition detailed in this paper all the results of this paper can be seen as providing an algebraic characterization of linear differential operators with selected symplectic or orthogonal differential galois groups

weighted shift and composition operators on lp which are m q isometries abstract we obtain some conditions about the weighted shift and the composition operators on l p to be m q isometries in particular we prove that if t is a strict 2 q isometry then p q whether t is a weighted shift or a composition operator on l p moreover we characterize the admissible weights for the weighted shift to be a strict 3 p isometry on l p the case of strict 4 p isometry is also studied

infinitesimal deformation of p adic differential equations on berkovich curves we show that if a differential equation mathscr f over a quasi smooth berkovich curve x has a certain compatibility condition with respect to an automorphism sigma of x then mathscr f acquires a semi linear action of sigma i e lifting that on x the compatibility condition forces the automorphism sigma to be close to the identity of x so the above construction applies to a certain class of automorphisms called infinitesimal this generalizes andre and di vizio asterisque 1 296 55 111 2004 and pulita compos math 144 4 867 919 2008 we also obtain an application to morita s p adic gamma function and to related values of p adic l functions

adaptive ar modeling in white gaussian noise autoregressive ar modeling is widely used in signal processing the coefficients of an ar model can be easily obtained with a least mean square lms prediction error filter however it is known that this filter gives a biased solution when the input signal is corrupted by white gaussian noise treichler 1979 suggested the spl gamma lms algorithm to remedy this problem and proved that the mean weight vector can converge to the wiener solution in this paper we develop a new algorithm that extends works of vijayan et al 1990 for adaptive ar modeling in the presence of white gaussian noise by theoretical analysis we show that the performance of the new algorithm is superior to the spl gamma lms filter simulations are also provided to support our theoretical results

isometric properties of elementary operators abstract we consider the elementary operator l acting on the hilbert schmidt class c 2 h given by l t atb with a and b bounded operators on h we establish necessary and sufficient conditions on a and b for l to be a 2 isometry or a 3 isometry we derive sufficient conditions for l to be an n isometry we also give several illustrative examples involving the weighted shift operator on l 2 and the multiplication operator on the dirichlet space

arithmetic invariants of discrete langlands parameters the local langlands correspondence can be used as a tool for making verifiable predictions about irreducible complex representations of p adic groups and their langlands parameters which are homomorphisms from the local weil deligne group to the l group in this article we refine a conjecture of hiraga ichino and ikeda which relates the formal degree of a discrete series representation to the value of the local gamma factor of its parameter we attach a rational function in x with rational coefficients to each discrete parameter which specializes at x q the cardinality of the residue field to the quotient of this local gamma factor by the gamma factor of the steinberg parameter the order of this rational function at x 0 is also an important invariant of the parameter it leads to a conjectural inequality for the swan conductor of a discrete parameter acting on the adjoint representation of the l group we verify this conjecture in many cases when we impose equality we obtain a prediction for the existence of simple wild parameters and simple supercuspidal representations both of which are found and described in this article

arithmetic theory of q difference equations the q analogue of grothendieck katz s conjecture on p curvatures grothendieck s conjecture on p curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places it is equivalent to katz s conjectural description of the generic galois group in this paper we prove an analogous statement for arithmetic q difference equation

c0 semigroups of m isometries on hilbert spaces abstract let t t t 0 be a c 0 semigroup on a separable hilbert space h we show that t t is an m isometry for any t if and only if the mapping t r t t x 2 for each x h is a polynomial of degree at most m this property is used to study m isometric right translation semigroup on weighted l p spaces we also provide alternative characterizations of the above property by imposing conditions on the infinitesimal generator operator and on the cogenerator operator of t t t 0 moreover we prove that a non unitary 2 isometry t on a hilbert space satisfying the kernel condition that is t t k e r t k e r t can be embedded into a c 0 semigroup if and only if d i m k e r t