structure arising from induction and jacquet modules of representations of classical p adic groups jacquet modules are very useful in the study of parabolically induced representations of reductive groups over a p adic field f we shall assume char f 2 in this paper it is very hard to describe explicitly the structure of jacquet modules of parabolically induced representations particularly in the most interesting cases there exists a description of factors of certain filtrations on them that description was done by j bernstein and a v zelevinsky in bz2 and by w casselman in c in the case of general linear groups the functor of parabolic induction and the jacquet functor induce a structure of z graded hopf algebra on the sum r of grothendieck groups of categories of smooth representations of gl n f s of finite length n 0 z1 the multiplication m r r r is defined using parabolic induction while the comultiplication m r r r is defined in terms of jacquet modules the most interesting part of the structure is the property that m r r r is a ring homomorphism hopf axiom this enables one to compute composition series of parabolically induced representations in a very simple way it is interesting to note that the existence of this strong structure did not have serious impact on the development of the representation theory of gl n f one of the reasons for that may lay in the fact that for gl n f there existed a very powerful theory of gelfandkazhdan derivatives and the main results of z1 were obtained using them nevertheless a v zelevinsky showed in z2 that some interesting parts of the representation theory of gl n over a finite field can be obtained as a structure theory of such hopf algebra defined in this setting besides that one of the main tools for the study of representation theory of gl n over a central division f algebra in t1 is such hopf algebra structure in this situation are not available gelfand kazhdan derivatives it is natural to ask does some structure of this kind exist for other simple split classical p adic groups since levi factors of classical groups are isomorphic to direct products of general linear groups and smaller groups from the same series one can expect for such structure to have some relation with r if it exists in the third section we define the direct sum of grothendieck groups r s which corresponds either to the series sp n f n 0 or so 2n 1 f n 0 in a similar way as r was defined for general linear groups the action of r on r s is defined using the parabolic induction in this way r s becomes z graded r module we can make r s a z graded comodule over r the comodule structure map r s r r s is again defined using the jacquet modules similarly as in the case of gl n f it is not hard to see that r s is not a hopf module over r see remark 7 3 in this paper we

jacquet modules of strongly positive representations of the metaplectic group strongly positive discrete series represent a particularly important class of irreducible square integrable representations of p adic groups indeed these representations are used as basic building blocks in known constructions of general discrete series in this paper we explicitly describe jacquet modules of strongly positive discrete series the obtained description of jacquet modules which relies on the classification of strongly positive discrete series given in 10 is valid in both classical and metaplectic case we expect that our results besides being interesting by themselves should be relevant to some potential applications in the theory of automorphic forms where both representations of metaplectic groups and structure of jacquet modules play an important part

strongly positive representations of gspin_ 2n 1 and the jacquet module method we explicitly construct the structure of jacquet modules of parabolically induced representations of gspin 2n 1 over a p adic field f of any characteristic using this construction of the jacquet module we obtain a classification of strongly positive representations of gspin 2n 1 over f and describe the general discrete series representations of gspin 2n 1 over f assuming the half integer conjecture one application of this paper is the proof of the equality of l functions from the langlands shahidi method and artin l functions through the local langlands correspondence kim in langlands shahidi l functions for gspin groups and the generic arthur packet conjecture preprint

logarithms of the derivative of univalent functions in qp spaces abstract for a univalent function d we study the membership of log to the space q p we look for geometric conditions and also a description involving the schwarzian derivative is given

locally univalent functions vmoa and the dirichlet space we study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g belongs either to the dirichlet space d vmoa or the little bloch space b 0 concerning vmoa and b 0 our findings generalize the corresponding results for conformal maps shown by pommerenke in the late 1970s in the case of d we give a strictly geometric necessary condition for g to satisfy log g is an element of d and also offer two different semi geometric characterizations of when log g is an element of d

forelli rudin estimates carleson measures and f p q s functions abstract a classical theorem of l carleson states that the injection map from the hardy space h p into l p d is bounded if and only if the positive measure on the unit disc is a bounded carleson measure in this paper forelli rudin estimates for arbitrary positive measures on the unit disc are proved and then these estimates are applied to characterize bounded s carleson measures in terms of bloch and f p q s functions

a review on singularly perturbed differential equations with turning points and interior layers singular perturbation problems with turning points arise as mathematical models for various physical phenomena the problem with interior turning point represent one dimensional version of stationary convection diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin boundary turning point problems on the other hand arise in geophysics and in modeling thermal boundary layers in laminar flow in this paper we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye towards the goal of developing general methods to solve such problems since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011

on an algebraic approach to the zelevinsky classification for classical p adic groups abstract in this paper we classify irreducible admissible representations of p adic classical groups in a purely algebraic way we present a new and simple algorithm for constructing the classifying data which is also useful in other contexts where the computation with jacquet modules or constant terms of eisenstein series appears we construct and study non standard intertwining operators they are defined in a purely algebraic way although their rationality follows from g muic a geometric construction of intertwining operators for reductive p adic groups manuscripta math 125 2008 241 272

dirichlet and vmoa domains via schwarzian derivative abstract short proofs of the following results concerning a bounded conformal map g of the unit disc d are presented 1 log g belongs to the dirichlet space if and only if the schwarzian derivative s g of g satisfies s g z 1 z 2 l 2 d 2 log g vmoa if and only if s g z 2 1 z 2 3 is a vanishing carleson measure on d analogous results for besov and q p 0 spaces are also given

a higher order method for stationary shock problems an equidistant finite difference method is proposed for quasilinear singularly perturbed boundary value problems the method uses a combination of one sided schemes and a third order three point scheme it is easy to implement and produces third order accuracy away from shocks

on a difference scheme of exponential type for a nonlinear singular perturbation problem a difference scheme of exponential type for solving a nonlinear singular perturbation problem is analysed although this scheme is not of monotone type al 1 convergence result is obtained relations between this scheme and engquist osher scheme are also discussed

finite difference schemes for quasilinear singular perturbation problems finite difference schemes for singularly perturbed quasilinear boundary value problems are considered the schemes have fitting factors which guarantee their uniform stability with respect to the perturbation parameter besides the usual stability in the discrete l1 norm we consider the maximum norm stability as well various schemes are compared numerically

a survey of numerical techniques for solving singularly perturbed ordinary differential equations this survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984 2000 the work done in this area during the period 1905 1984 has already been surveyed by the first author of this paper see appl math comput 30 1989 223 for details due to the space constraints we have covered only singularly perturbed one dimensional problems

on the non unitary unramified dual for classical p adic groups in this paper we give a zelevinsky type classification of unramified irreducible representations of split classical groups

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

stability of a streamline diffusion finite element method for turning point problems a one dimensional singularly perturbed problem with a boundary turning point is considered in this paper let v h be the linear finite element space on a suitable grid t h a variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation u h satisfies u u email protected

analysis of difference schemes for a stationary shock problem we consider the limit function u of the solutions u varepsilon of a singularly perturbed boundary value problem in general u will be discontinuous two difference approximations of the boundary value problem are studied and the discrete values for varepsilon 0 h to 0 are compared with u error estimates of order o h and o h 2 are proved and the sharpness of numerical layers is established

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

nonlinear singular perturbation problems and one sided difference schemes we consider the boundary value problem varepsilon y a y y b x y f x 1 leqq x leqq 1 for y 1 and y 1 given and b x 0 equiv 0 b y x y geqq 0 we construct a simple difference scheme approximating varepsilon u xx a u u x b x u f x u t for t geqq 0 1 leqq x leqq 1 with the same boundary conditions and an arbitrary initial guess as the numerical artificial time approaches infinity we prove convergence to a unique steady state solution as the mesh size delta x and the parameter varepsilon approach zero in any order we prove convergence to the solution of the corresponding o d e we use one sided differences to approximate the transport term the method applies equally well to multidimensional analogues we present numerical results verifying the theory

monotone difference schemes for singular perturbation problems we consider numerical solutions of the boundary value problem varepsilon y f y b x y 0 0 leqq x leqq 1 y 0 a y 1 b varepsilon 0 b y geqq delta 0 with monotone difference schemes on nonuniform grids we prove general convergence results and show that the engquist osher monotone scheme will reproduce essential properties of the true solution for any grid for the inversion of the nonlinear scheme we suggest implicit time relaxation with variable time steps

parabolic induction and jacquet functors for metaplectic groups abstract in this paper we give a new formulation of a geometric lemma for the metaplectic groups over p adic field f analogous to the existing one for classical groups this enables us to give a zelevinsky type classification of irreducible admissible genuine representations of metaplectic groups as an application of our jacquet module technique we explicitly calculate jacquet modules of even and odd weil representations

some improvements of the nonequidistant engquist osher scheme two nonequidistant finite difference schemes for quasilinear singular perturbation problems are given and their properties are discussed and compared one of them corresponds to the equidistant lorenz modification of the engquist osher scheme the other one switches in dependence on the cell reynolds number both schemes show quadratic l 1 accuracy but the second one gives better pointwise results

numerical solution of quasilinear attractive turning point problems abstract a quasilinear singularity perturbed boundary value problem with a turning point of the attractive type is considered analytic properties of its solution are established and used for the construction of a numerical method uniform in the perturbation parameter the paper is an extension of a result obtained previously for the semilinear case

schwarzian derivative and general besov type domains abstract we study univalent functions f for which log f belongs to a class of general besov type spaces we give a characterization of the general besov type domains in terms of carleson measure conditions on the schwarzian derivative s f and mention some further connection to teichmuller theory

strongly positive representations of metaplectic groups abstract in this paper we obtain a classification of irreducible strongly positive square integrable genuine representations of metaplectic groups over p adic fields using a purely algebraic approach our results parallel those of m glin and tadic for classical groups but their work relies on certain conjectures on the other hand our results are complete and there are no additional conditions or hypotheses the important point to note here is that our results and techniques can be used in the case of classical p adic groups in a completely analogous manner